LMFDB - Embedded newform 87.2.k.a.8.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [87,2,Mod(2,87)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("87.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(87, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([14, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.k (of order $28$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			8.7
Character	$\chi$	$=$	87.8
Dual form			87.2.k.a.11.7

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.576259 - 1.64685i) q^{2} +(-0.221759 - 1.71780i) q^{3} +(-0.816387 - 0.651047i) q^{4} +(-1.59790 + 0.769508i) q^{5} +(-2.95675 - 0.624690i) q^{6} +(1.54710 + 1.94000i) q^{7} +(1.41204 - 0.887242i) q^{8} +(-2.90165 + 0.761874i) q^{9} +(0.346463 + 3.07494i) q^{10} +(1.02572 + 0.644501i) q^{11} +(-0.937325 + 1.54676i) q^{12} +(-1.08029 + 0.246570i) q^{13} +(4.08643 - 1.42990i) q^{14} +(1.67621 + 2.57422i) q^{15} +(-1.11217 - 4.87274i) q^{16} +(2.39140 - 2.39140i) q^{17} +(-0.417404 + 5.21762i) q^{18} +(0.482698 - 0.0543871i) q^{19} +(1.80549 + 0.412091i) q^{20} +(2.98944 - 3.08782i) q^{21} +(1.65248 - 1.31781i) q^{22} +(-3.99989 + 8.30586i) q^{23} +(-1.83723 - 2.22884i) q^{24} +(-1.15631 + 1.44997i) q^{25} +(-0.216464 + 1.92117i) q^{26} +(1.95221 + 4.81548i) q^{27} -2.59103i q^{28} +(5.27938 - 1.06215i) q^{29} +(5.20529 - 1.27705i) q^{30} +(-9.19909 - 3.21890i) q^{31} +(-5.35125 - 0.602941i) q^{32} +(0.879658 - 1.90490i) q^{33} +(-2.56022 - 5.31635i) q^{34} +(-3.96496 - 1.90942i) q^{35} +(2.86488 + 1.26712i) q^{36} +(4.30274 + 6.84777i) q^{37} +(0.188592 - 0.826274i) q^{38} +(0.663123 + 1.80105i) q^{39} +(-1.57355 + 2.50430i) q^{40} +(-6.28241 - 6.28241i) q^{41} +(-3.36249 - 6.70256i) q^{42} +(-1.18857 - 3.39673i) q^{43} +(-0.417782 - 1.19395i) q^{44} +(4.05027 - 3.45024i) q^{45} +(11.3736 + 11.3736i) q^{46} +(-2.28637 + 3.63873i) q^{47} +(-8.12373 + 2.99106i) q^{48} +(0.187557 - 0.821739i) q^{49} +(1.72155 + 2.73983i) q^{50} +(-4.63825 - 3.57762i) q^{51} +(1.04247 + 0.502026i) q^{52} +(-5.08537 - 10.5599i) q^{53} +(9.05537 - 0.440041i) q^{54} +(-2.13494 - 0.240550i) q^{55} +(3.90581 + 1.36670i) q^{56} +(-0.200469 - 0.817117i) q^{57} +(1.29308 - 9.30643i) q^{58} -2.84288i q^{59} +(0.307505 - 3.19285i) q^{60} +(0.299240 - 2.65582i) q^{61} +(-10.6021 + 13.2946i) q^{62} +(-5.96717 - 4.45050i) q^{63} +(0.260480 - 0.540893i) q^{64} +(1.53646 - 1.22529i) q^{65} +(-2.63017 - 2.54638i) q^{66} +(11.9366 + 2.72445i) q^{67} +(-3.50922 + 0.395394i) q^{68} +(15.1548 + 5.02910i) q^{69} +(-5.42938 + 5.42938i) q^{70} +(1.90444 + 8.34388i) q^{71} +(-3.42126 + 3.65026i) q^{72} +(1.41405 - 0.494798i) q^{73} +(13.7568 - 3.13989i) q^{74} +(2.74717 + 1.66476i) q^{75} +(-0.429477 - 0.269859i) q^{76} +(0.336554 + 2.98700i) q^{77} +(3.34819 - 0.0541966i) q^{78} +(1.96273 - 1.23326i) q^{79} +(5.52674 + 6.93032i) q^{80} +(7.83910 - 4.42138i) q^{81} +(-13.9665 + 6.72591i) q^{82} +(-6.97313 - 5.56088i) q^{83} +(-4.45086 + 0.574585i) q^{84} +(-1.98101 + 5.66141i) q^{85} -6.27884 q^{86} +(-2.99531 - 8.83335i) q^{87} +2.02018 q^{88} +(-3.09433 + 8.84308i) q^{89} +(-3.34803 - 8.65843i) q^{90} +(-2.14967 - 1.71431i) q^{91} +(8.67297 - 4.17668i) q^{92} +(-3.48943 + 16.5160i) q^{93} +(4.67492 + 5.86216i) q^{94} +(-0.729452 + 0.458345i) q^{95} +(0.150959 + 9.32607i) q^{96} +(-0.582251 - 5.16762i) q^{97} +(-1.24520 - 0.782413i) q^{98} +(-3.46730 - 1.08865i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{3} - 28 q^{4} - 14 q^{6} - 20 q^{7} - 14 q^{9} - 4 q^{10} - 8 q^{12} - 28 q^{13} - 16 q^{15} - 48 q^{16} - 28 q^{18} - 20 q^{19} + 26 q^{21} - 28 q^{22} + 58 q^{24} - 20 q^{25} + 36 q^{27}+ \cdots + 82 q^{99}+O(q^{100}) $ 96 * q - 12 * q^3 - 28 * q^4 - 14 * q^6 - 20 * q^7 - 14 * q^9 - 4 * q^10 - 8 * q^12 - 28 * q^13 - 16 * q^15 - 48 * q^16 - 28 * q^18 - 20 * q^19 + 26 * q^21 - 28 * q^22 + 58 * q^24 - 20 * q^25 + 36 * q^27 + 96 * q^30 - 32 * q^31 + 28 * q^33 - 28 * q^34 + 22 * q^36 - 4 * q^37 - 40 * q^39 - 48 * q^40 - 14 * q^42 - 32 * q^43 + 42 * q^45 + 120 * q^46 - 20 * q^48 + 4 * q^49 - 14 * q^51 + 72 * q^52 - 30 * q^54 + 148 * q^55 + 112 * q^58 + 20 * q^60 + 12 * q^61 - 14 * q^63 + 224 * q^64 - 32 * q^66 + 28 * q^67 + 10 * q^69 + 52 * q^70 - 44 * q^72 + 16 * q^73 - 144 * q^75 - 100 * q^76 - 102 * q^78 - 60 * q^79 - 146 * q^81 - 108 * q^82 - 64 * q^84 - 104 * q^85 - 70 * q^87 - 312 * q^88 - 96 * q^90 - 112 * q^91 - 70 * q^93 + 56 * q^94 - 168 * q^96 + 32 * q^97 + 82 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{3}{28}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.576259	−	1.64685i	0.407476	−	1.16450i	−0.539162	−	0.842202i	$-0.681259\pi$
$2$	0.576259	−	1.64685i	0.407476	−	1.16450i	0.946638	−	0.322299i	$-0.104455\pi$
$3$	−0.221759	−	1.71780i	−0.128033	−	0.991770i
$3$	−0.221759	−	1.71780i	−0.128033	−	0.991770i
$4$	−0.816387	−	0.651047i	−0.408194	−	0.325524i
$5$	−1.59790	+	0.769508i	−0.714602	+	0.344134i	−0.755608	−	0.655025i	$-0.772658\pi$
$5$	−1.59790	+	0.769508i	−0.714602	+	0.344134i	0.0410052	+	0.999159i	$0.486944\pi$
$6$	−2.95675	−	0.624690i	−1.20709	−	0.255029i
$7$	1.54710	+	1.94000i	0.584749	+	0.733252i	0.982915	−	0.184062i	$-0.0589246\pi$
$7$	1.54710	+	1.94000i	0.584749	+	0.733252i	−0.398166	+	0.917313i	$0.630353\pi$
$8$	1.41204	−	0.887242i	0.499231	−	0.313687i
$9$	−2.90165	+	0.761874i	−0.967215	+	0.253958i
$10$	0.346463	+	3.07494i	0.109561	+	0.972382i
$11$	1.02572	+	0.644501i	0.309265	+	0.194324i	0.677717	−	0.735322i	$-0.262969\pi$
$11$	1.02572	+	0.644501i	0.309265	+	0.194324i	−0.368452	+	0.929647i	$0.620112\pi$
$12$	−0.937325	+	1.54676i	−0.270582	+	0.446512i
$13$	−1.08029	+	0.246570i	−0.299620	+	0.0683863i	−0.369688	−	0.929156i	$-0.620535\pi$
$13$	−1.08029	+	0.246570i	−0.299620	+	0.0683863i	0.0700682	+	0.997542i	$0.477678\pi$
$14$	4.08643	−	1.42990i	1.09214	−	0.382158i
$15$	1.67621	+	2.57422i	0.432795	+	0.664661i
$16$	−1.11217	−	4.87274i	−0.278042	−	1.21818i
$17$	2.39140	−	2.39140i	0.579999	−	0.579999i	−0.354904	−	0.934903i	$-0.615486\pi$
$17$	2.39140	−	2.39140i	0.579999	−	0.579999i	0.934903	+	0.354904i	$0.115486\pi$
$18$	−0.417404	+	5.21762i	−0.0983831	+	1.22980i
$19$	0.482698	−	0.0543871i	0.110739	−	0.0124772i	−0.0564212	−	0.998407i	$-0.517969\pi$
$19$	0.482698	−	0.0543871i	0.110739	−	0.0124772i	0.167160	+	0.985930i	$0.446540\pi$
$20$	1.80549	+	0.412091i	0.403720	+	0.0921465i
$21$	2.98944	−	3.08782i	0.652350	−	0.673817i
$22$	1.65248	−	1.31781i	0.352309	−	0.280957i
$23$	−3.99989	+	8.30586i	−0.834035	+	1.73189i	−0.168257	+	0.985743i	$0.553814\pi$
$23$	−3.99989	+	8.30586i	−0.834035	+	1.73189i	−0.665779	+	0.746149i	$0.731901\pi$
$24$	−1.83723	−	2.22884i	−0.375024	−	0.454960i
$25$	−1.15631	+	1.44997i	−0.231262	+	0.289993i
$26$	−0.216464	+	1.92117i	−0.0424522	+	0.376773i
$27$	1.95221	+	4.81548i	0.375703	+	0.926740i
$28$		−	2.59103i		−	0.489658i
$29$	5.27938	−	1.06215i	0.980356	−	0.197236i
$29$	5.27938	−	1.06215i	0.980356	−	0.197236i
$30$	5.20529	−	1.27705i	0.950352	−	0.233156i
$31$	−9.19909	−	3.21890i	−1.65221	−	0.578132i	−0.666337	−	0.745651i	$-0.732139\pi$
$31$	−9.19909	−	3.21890i	−1.65221	−	0.578132i	−0.985869	+	0.167520i	$0.946424\pi$
$32$	−5.35125	−	0.602941i	−0.945977	−	0.106586i
$33$	0.879658	−	1.90490i	0.153129	−	0.331600i
$34$	−2.56022	−	5.31635i	−0.439074	−	0.911746i
$35$	−3.96496	−	1.90942i	−0.670200	−	0.322751i
$36$	2.86488	+	1.26712i	0.477480	+	0.211187i
$37$	4.30274	+	6.84777i	0.707366	+	1.12577i	0.986221	+	0.165434i	$0.0529024\pi$
$37$	4.30274	+	6.84777i	0.707366	+	1.12577i	−0.278855	+	0.960333i	$0.589955\pi$
$38$	0.188592	−	0.826274i	0.0305936	−	0.134039i
$39$	0.663123	+	1.80105i	0.106185	+	0.288398i
$40$	−1.57355	+	2.50430i	−0.248801	+	0.395964i
$41$	−6.28241	−	6.28241i	−0.981148	−	0.981148i	0.0186776	−	0.999826i	$-0.494054\pi$
$41$	−6.28241	−	6.28241i	−0.981148	−	0.981148i	−0.999826	+	0.0186776i	$0.994054\pi$
$42$	−3.36249	−	6.70256i	−0.518843	−	1.03423i
$43$	−1.18857	−	3.39673i	−0.181255	−	0.517997i	0.817026	−	0.576600i	$-0.195621\pi$
$43$	−1.18857	−	3.39673i	−0.181255	−	0.517997i	−0.998281	+	0.0586033i	$0.981335\pi$
$44$	−0.417782	−	1.19395i	−0.0629830	−	0.179995i
$45$	4.05027	−	3.45024i	0.603779	−	0.514331i
$46$	11.3736	+	11.3736i	1.67694	+	1.67694i
$47$	−2.28637	+	3.63873i	−0.333501	+	0.530764i	−0.970812	−	0.239843i	$-0.922904\pi$
$47$	−2.28637	+	3.63873i	−0.333501	+	0.530764i	0.637311	+	0.770607i	$0.280047\pi$
$48$	−8.12373	+	2.99106i	−1.17256	+	0.431722i
$49$	0.187557	−	0.821739i	0.0267938	−	0.117391i
$50$	1.72155	+	2.73983i	0.243463	+	0.387470i
$51$	−4.63825	−	3.57762i	−0.649485	−	0.500967i
$52$	1.04247	+	0.502026i	0.144564	+	0.0696185i
$53$	−5.08537	−	10.5599i	−0.698530	−	1.45051i	−0.883820	−	0.467828i	$-0.845037\pi$
$53$	−5.08537	−	10.5599i	−0.698530	−	1.45051i	0.185290	−	0.982684i	$-0.440678\pi$
$54$	9.05537	−	0.440041i	1.23228	−	0.0598820i
$55$	−2.13494	−	0.240550i	−0.287875	−	0.0324358i
$56$	3.90581	+	1.36670i	0.521936	+	0.182633i
$57$	−0.200469	−	0.817117i	−0.0265527	−	0.108230i
$58$	1.29308	−	9.30643i	0.169790	−	1.22199i
$59$		−	2.84288i		−	0.370111i	−0.982728	−	0.185056i	$-0.940754\pi$
$59$		−	2.84288i		−	0.370111i	0.982728	−	0.185056i	$-0.0592465\pi$
$60$	0.307505	−	3.19285i	0.0396987	−	0.412195i
$61$	0.299240	−	2.65582i	0.0383137	−	0.340043i	−0.959902	−	0.280335i	$-0.909554\pi$
$61$	0.299240	−	2.65582i	0.0383137	−	0.340043i	0.998216	−	0.0597083i	$-0.0190170\pi$
$62$	−10.6021	+	13.2946i	−1.34647	+	1.68842i
$63$	−5.96717	−	4.45050i	−0.751793	−	0.560711i
$64$	0.260480	−	0.540893i	0.0325600	−	0.0676116i
$65$	1.53646	−	1.22529i	0.190575	−	0.151978i
$66$	−2.63017	−	2.54638i	−0.323752	−	0.313438i
$67$	11.9366	+	2.72445i	1.45829	+	0.332844i	0.876857	−	0.480752i	$-0.159636\pi$
$67$	11.9366	+	2.72445i	1.45829	+	0.332844i	0.581430	+	0.813596i	$0.302493\pi$
$68$	−3.50922	+	0.395394i	−0.425555	+	0.0479486i
$69$	15.1548	+	5.02910i	1.82442	+	0.605432i
$70$	−5.42938	+	5.42938i	−0.648935	+	0.648935i
$71$	1.90444	+	8.34388i	0.226015	+	0.990236i	0.952854	+	0.303428i	$0.0981313\pi$
$71$	1.90444	+	8.34388i	0.226015	+	0.990236i	−0.726839	+	0.686808i	$0.759012\pi$
$72$	−3.42126	+	3.65026i	−0.403200	+	0.430187i
$73$	1.41405	−	0.494798i	0.165502	−	0.0579118i	−0.246256	−	0.969205i	$-0.579200\pi$
$73$	1.41405	−	0.494798i	0.165502	−	0.0579118i	0.411758	+	0.911293i	$0.364915\pi$
$74$	13.7568	−	3.13989i	1.59919	−	0.365005i
$75$	2.74717	+	1.66476i	0.317215	+	0.192230i
$76$	−0.429477	−	0.269859i	−0.0492644	−	0.0309549i
$77$	0.336554	+	2.98700i	0.0383539	+	0.340400i
$78$	3.34819	−	0.0541966i	0.379108	−	0.00613655i
$79$	1.96273	−	1.23326i	0.220824	−	0.138753i	−0.417077	−	0.908871i	$-0.636946\pi$
$79$	1.96273	−	1.23326i	0.220824	−	0.138753i	0.637901	+	0.770118i	$0.279803\pi$
$80$	5.52674	+	6.93032i	0.617909	+	0.774833i
$81$	7.83910	−	4.42138i	0.871011	−	0.491264i
$82$	−13.9665	+	6.72591i	−1.54234	+	0.742753i
$83$	−6.97313	−	5.56088i	−0.765400	−	0.610386i	0.160988	−	0.986956i	$-0.448532\pi$
$83$	−6.97313	−	5.56088i	−0.765400	−	0.610386i	−0.926388	+	0.376570i	$0.877103\pi$
$84$	−4.45086	+	0.574585i	−0.485628	+	0.0626923i
$85$	−1.98101	+	5.66141i	−0.214871	+	0.614067i
$86$	−6.27884			−0.677065
$87$	−2.99531	−	8.83335i	−0.321131	−	0.947035i
$88$	2.02018			0.215352
$89$	−3.09433	+	8.84308i	−0.327998	+	0.937365i	0.655301	+	0.755368i	$0.272542\pi$
$89$	−3.09433	+	8.84308i	−0.327998	+	0.937365i	−0.983299	+	0.181997i	$0.941744\pi$
$90$	−3.34803	−	8.65843i	−0.352913	−	0.912678i
$91$	−2.14967	−	1.71431i	−0.225347	−	0.179708i
$92$	8.67297	−	4.17668i	0.904220	−	0.435449i
$93$	−3.48943	+	16.5160i	−0.361837	+	1.71263i
$94$	4.67492	+	5.86216i	0.482181	+	0.604636i
$95$	−0.729452	+	0.458345i	−0.0748402	+	0.0470252i
$96$	0.150959	+	9.32607i	0.0154072	+	0.951838i
$97$	−0.582251	−	5.16762i	−0.0591186	−	0.524692i	−0.988016	−	0.154354i	$-0.950670\pi$
$97$	−0.582251	−	5.16762i	−0.0591186	−	0.524692i	0.928897	−	0.370338i	$-0.120758\pi$
$98$	−1.24520	−	0.782413i	−0.125784	−	0.0790356i
$99$	−3.46730	−	1.08865i	−0.348476	−	0.109413i
$100$	1.88799	−	0.430922i	0.188799	−	0.0430922i
$101$	11.4685	−	4.01299i	1.14116	−	0.399308i	0.307476	−	0.951556i	$-0.400516\pi$
$101$	11.4685	−	4.01299i	1.14116	−	0.399308i	0.833680	+	0.552248i	$0.186230\pi$
$102$	−8.56464	+	5.57688i	−0.848026	+	0.552193i
$103$	2.53000	+	11.0847i	0.249288	+	1.09220i	0.932269	+	0.361767i	$0.117826\pi$
$103$	2.53000	+	11.0847i	0.249288	+	1.09220i	−0.682980	+	0.730437i	$0.739317\pi$
$104$	−1.30665	+	1.30665i	−0.128127	+	0.128127i
$105$	−2.40073	+	7.23442i	−0.234288	+	0.706007i
$106$	−20.3211	+	2.28963i	−1.97376	+	0.222389i
$107$	−1.16741	−	0.266455i	−0.112858	−	0.0257592i	0.165719	−	0.986173i	$-0.447006\pi$
$107$	−1.16741	−	0.266455i	−0.112858	−	0.0257592i	−0.278577	+	0.960414i	$0.589863\pi$
$108$	1.54135	−	5.20228i	0.148316	−	0.500590i
$109$	8.29478	−	6.61487i	0.794496	−	0.633589i	−0.139763	−	0.990185i	$-0.544634\pi$
$109$	8.29478	−	6.61487i	0.794496	−	0.633589i	0.934259	+	0.356596i	$0.116063\pi$
$110$	−1.62643	+	3.37731i	−0.155074	+	0.322014i
$111$	10.8089	−	8.90979i	1.02594	−	0.845680i
$112$	7.73248	−	9.69622i	0.730651	−	0.916207i
$113$	0.516504	−	4.58410i	0.0485886	−	0.431236i	−0.945743	−	0.324915i	$-0.894664\pi$
$113$	0.516504	−	4.58410i	0.0485886	−	0.431236i	0.994332	−	0.106321i	$-0.0339071\pi$
$114$	−1.46119	−	0.140728i	−0.136853	−	0.0131804i
$115$		−	16.3499i		−	1.52463i
$116$	−5.00153	−	2.57000i	−0.464380	−	0.238618i
$117$	2.94678	−	1.53851i	0.272430	−	0.142235i
$118$	−4.68180	−	1.63823i	−0.430995	−	0.150812i
$119$	8.33905	+	0.939585i	0.764440	+	0.0861316i
$120$	4.65082	+	2.14769i	0.424560	+	0.196057i
$121$	−4.13601	−	8.58851i	−0.376001	−	0.780773i
$122$	−4.20131	−	2.02325i	−0.380369	−	0.183176i
$123$	−9.39872	+	12.1851i	−0.847454	+	1.09869i
$124$	5.41436	+	8.61691i	0.486224	+	0.773821i
$125$	2.70515	−	11.8520i	0.241956	−	1.06008i
$126$	−10.7680	+	7.26242i	−0.959286	+	0.646988i
$127$	1.38905	−	2.21065i	0.123258	−	0.196164i	−0.779395	−	0.626532i	$-0.784474\pi$
$127$	1.38905	−	2.21065i	0.123258	−	0.196164i	0.902653	+	0.430369i	$0.141616\pi$
$128$	−8.35637	−	8.35637i	−0.738605	−	0.738605i
$129$	−5.57132	+	2.79498i	−0.490527	+	0.246084i
$130$	−1.13247	−	3.23641i	−0.0993242	−	0.283852i
$131$	0.142233	+	0.406478i	0.0124269	+	0.0355142i	0.949930	−	0.312464i	$-0.101154\pi$
$131$	0.142233	+	0.406478i	0.0124269	+	0.0355142i	−0.937503	+	0.347978i	$0.886868\pi$
$132$	−1.95832	+	0.982434i	−0.170450	+	0.0855099i
$133$	0.852294	+	0.852294i	0.0739033	+	0.0739033i
$134$	11.3653	−	18.0878i	0.981815	−	1.56255i
$135$	−6.82499	−	6.19242i	−0.587401	−	0.532958i
$136$	1.25499	−	5.49849i	0.107615	−	0.471492i
$137$	2.75997	+	4.39247i	0.235800	+	0.375274i	0.943572	−	0.331167i	$-0.107442\pi$
$137$	2.75997	+	4.39247i	0.235800	+	0.375274i	−0.707772	+	0.706441i	$0.750299\pi$
$138$	17.0153	−	22.0597i	1.44844	−	1.87784i
$139$	−5.43195	−	2.61589i	−0.460732	−	0.221877i	0.189095	−	0.981959i	$-0.439445\pi$
$139$	−5.43195	−	2.61589i	−0.460732	−	0.221877i	−0.649827	+	0.760082i	$0.725159\pi$
$140$	1.99382	+	4.14020i	0.168508	+	0.349911i
$141$	6.75763	+	3.12059i	0.569095	+	0.262801i
$142$	14.8386	+	1.67191i	1.24523	+	0.140303i
$143$	−1.26699	−	0.443339i	−0.105951	−	0.0370739i
$144$	6.93953	+	13.2916i	0.578295	+	1.10763i
$145$	−7.61858	+	5.75973i	−0.632689	+	0.478320i
$146$		−	2.61387i		−	0.216325i
$147$	−1.45317	−	0.139956i	−0.119856	−	0.0115434i
$148$	0.945520	−	8.39172i	0.0777213	−	0.689795i
$149$	2.74781	−	3.44564i	0.225109	−	0.282278i	−0.656432	−	0.754385i	$-0.727935\pi$
$149$	2.74781	−	3.44564i	0.225109	−	0.282278i	0.881541	+	0.472107i	$0.156507\pi$
$150$	4.32469	−	3.56485i	0.353110	−	0.291069i
$151$	−3.83234	+	7.95793i	−0.311871	+	0.647607i	−0.996707	−	0.0810904i	$-0.974160\pi$
$151$	−3.83234	+	7.95793i	−0.311871	+	0.647607i	0.684836	+	0.728698i	$0.259874\pi$
$152$	0.633334	−	0.505067i	0.0513701	−	0.0409663i
$153$	−5.11705	+	8.76094i	−0.413689	+	0.708280i
$154$	5.11309	+	1.16703i	0.412025	+	0.0940420i
$155$	17.1762	−	1.93529i	1.37962	−	0.155446i
$156$	0.631201	−	1.90208i	0.0505365	−	0.152288i
$157$	−7.17901	+	7.17901i	−0.572948	+	0.572948i	−0.932951	−	0.360003i	$-0.882776\pi$
$157$	−7.17901	+	7.17901i	−0.572948	+	0.572948i	0.360003	+	0.932951i	$0.382776\pi$
$158$	−0.899964	−	3.94300i	−0.0715973	−	0.313688i
$159$	−17.0120	+	11.0774i	−1.34914	+	0.878494i
$160$	9.01473	−	3.15439i	0.712677	−	0.249377i
$161$	−22.3016	+	5.09020i	−1.75761	+	0.401164i
$162$	−2.76401	−	15.4577i	−0.217161	−	1.21447i
$163$	−3.44823	−	2.16667i	−0.270086	−	0.169706i	0.390179	−	0.920739i	$-0.372413\pi$
$163$	−3.44823	−	2.16667i	−0.270086	−	0.169706i	−0.660265	+	0.751033i	$0.729556\pi$
$164$	1.03874	+	9.21903i	0.0811116	+	0.719885i
$165$	0.0602269	+	3.72074i	0.00468866	+	0.289659i
$166$	−13.1763	+	8.27920i	−1.02268	+	0.642591i
$167$	12.6392	+	15.8490i	0.978047	+	1.22643i	0.974025	+	0.226440i	$0.0727087\pi$
$167$	12.6392	+	15.8490i	0.978047	+	1.22643i	0.00402168	+	0.999992i	$0.498720\pi$
$168$	1.48157	−	7.01247i	0.114305	−	0.541024i
$169$	−10.6064	+	5.10775i	−0.815874	+	0.392904i
$170$	8.18194	+	6.52488i	0.627526	+	0.500435i
$171$	−1.35918	+	0.525567i	−0.103939	+	0.0401912i
$172$	−1.24110	+	3.54686i	−0.0946331	+	0.270446i
$173$	3.30578			0.251334			0.125667	−	0.992072i	$-0.459893\pi$
$173$	3.30578			0.251334			0.125667	+	0.992072i	$0.459893\pi$
$174$	−16.2733	−	0.157466i	−1.23368	−	0.0119375i
$175$	−4.60186			−0.347868
$176$	1.99971	−	5.71484i	0.150734	−	0.430772i
$177$	−4.88348	+	0.630434i	−0.367065	+	0.0473863i
$178$	12.7801	+	10.1918i	0.957910	+	0.763908i
$179$	−4.99423	+	2.40509i	−0.373286	+	0.179765i	−0.611115	−	0.791542i	$-0.709279\pi$
$179$	−4.99423	+	2.40509i	−0.373286	+	0.179765i	0.237829	+	0.971307i	$0.423564\pi$
$180$	−5.55286	+	0.179813i	−0.413885	+	0.0134025i
$181$	−4.91454	−	6.16264i	−0.365295	−	0.458065i	0.564885	−	0.825170i	$-0.308921\pi$
$181$	−4.91454	−	6.16264i	−0.365295	−	0.458065i	−0.930180	+	0.367105i	$0.880349\pi$
$182$	−4.06197	+	2.55231i	−0.301094	+	0.189190i
$183$	−4.62852	+	0.0749211i	−0.342150	+	0.00553833i
$184$	1.72131	+	15.2771i	0.126897	+	1.12624i
$185$	−12.1448	−	7.63106i	−0.892901	−	0.561047i
$186$	25.1886	+	15.2641i	1.84692	+	1.11922i
$187$	3.99416	−	0.911640i	0.292082	−	0.0666657i
$188$	4.23555	−	1.48208i	0.308909	−	0.108092i
$189$	−6.32178	+	11.2373i	−0.459842	+	0.817395i
$190$	0.334474	+	1.46543i	0.0242653	+	0.106313i
$191$	−6.59651	+	6.59651i	−0.477307	+	0.477307i	−0.904269	−	0.426963i	$-0.859584\pi$
$191$	−6.59651	+	6.59651i	−0.477307	+	0.477307i	0.426963	+	0.904269i	$0.359584\pi$
$192$	−0.986907	−	0.327504i	−0.0712239	−	0.0236356i
$193$	11.7855	−	1.32791i	0.848338	−	0.0955847i	0.322917	−	0.946427i	$-0.395337\pi$
$193$	11.7855	−	1.32791i	0.848338	−	0.0955847i	0.525421	+	0.850843i	$0.323908\pi$
$194$	−8.84584	−	2.01900i	−0.635094	−	0.144956i
$195$	−2.44552	−	2.36761i	−0.175127	−	0.169548i
$196$	−0.688110	+	0.548749i	−0.0491507	+	0.0391964i
$197$	−1.76954	+	3.67449i	−0.126075	+	0.261797i	−0.954447	−	0.298382i	$-0.903553\pi$
$197$	−1.76954	+	3.67449i	−0.126075	+	0.261797i	0.828372	+	0.560179i	$0.189267\pi$
$198$	−3.79090	+	5.08278i	−0.269407	+	0.361218i
$199$	6.84164	−	8.57915i	0.484991	−	0.608160i	−0.477779	−	0.878480i	$-0.658558\pi$
$199$	6.84164	−	8.57915i	0.484991	−	0.608160i	0.962770	+	0.270320i	$0.0871296\pi$
$200$	−0.346281	+	3.07333i	−0.0244858	+	0.217317i
$201$	2.03300	−	21.1088i	0.143397	−	1.48890i
$202$		−	21.1994i		−	1.49159i
$203$	10.2283	+	8.59875i	0.717886	+	0.603514i
$204$	1.45741	+	5.94044i	0.102039	+	0.415914i
$205$	14.8730	+	5.20430i	1.03878	+	0.363484i
$206$	19.7127	+	2.22109i	1.37345	+	0.154751i
$207$	5.27825	−	27.1481i	0.366864	−	1.88692i
$208$	2.40294	+	4.98976i	0.166614	+	0.345978i
$209$	0.530165	+	0.255314i	0.0366722	+	0.0176604i
$210$	10.5306	+	8.12255i	0.726679	+	0.560509i
$211$	13.1840	+	20.9822i	0.907622	+	1.44447i	0.895758	+	0.444542i	$0.146634\pi$
$211$	13.1840	+	20.9822i	0.907622	+	1.44447i	0.0118637	+	0.999930i	$0.496224\pi$
$212$	−2.72335	+	11.9318i	−0.187040	+	0.819478i
$213$	13.9108	−	5.12176i	0.953149	−	0.350937i
$214$	−1.11154	+	1.76901i	−0.0759836	+	0.120927i
$215$	4.51303	+	4.51303i	0.307786	+	0.307786i
$216$	7.02909	+	5.06756i	0.478269	+	0.344804i
$217$	−7.98724	−	22.8262i	−0.542209	−	1.54954i
$218$	−6.11377	−	17.4722i	−0.414077	−	1.18336i
$219$	−1.16354	−	2.31933i	−0.0786249	−	0.156726i
$220$	1.58633	+	1.58633i	0.106950	+	0.106950i
$221$	−1.99377	+	3.17306i	−0.134115	+	0.213443i
$222$	−8.44438	−	22.9350i	−0.566750	−	1.53930i
$223$	−4.07939	+	17.8730i	−0.273176	+	1.19686i	0.633063	+	0.774100i	$0.281797\pi$
$223$	−4.07939	+	17.8730i	−0.273176	+	1.19686i	−0.906240	+	0.422764i	$0.861060\pi$
$224$	−7.10922	−	11.3143i	−0.475005	−	0.755965i
$225$	2.25051	−	5.08825i	0.150034	−	0.339216i
$226$	−7.25170	−	3.49224i	−0.482376	−	0.232300i
$227$	10.5337	+	21.8734i	0.699145	+	1.45179i	0.883259	+	0.468884i	$0.155344\pi$
$227$	10.5337	+	21.8734i	0.699145	+	1.45179i	−0.184115	+	0.982905i	$0.558942\pi$
$228$	−0.368321	+	0.797598i	−0.0243927	+	0.0528222i
$229$	−6.13894	−	0.691693i	−0.405673	−	0.0457084i	−0.0932293	−	0.995645i	$-0.529719\pi$
$229$	−6.13894	−	0.691693i	−0.405673	−	0.0457084i	−0.312444	+	0.949936i	$0.601148\pi$
$230$	−26.9259	−	9.42176i	−1.77544	−	0.621253i
$231$	5.05642	−	1.24053i	0.332688	−	0.0816206i
$232$	6.51229	−	6.18388i	0.427553	−	0.405992i
$233$			13.5660i			0.888735i	0.895845	+	0.444368i	$0.146572\pi$
$233$			13.5660i			0.888735i	−0.895845	+	0.444368i	$0.853428\pi$
$234$	−0.835590	−	5.73949i	−0.0546243	−	0.375202i
$235$	0.853352	−	7.57371i	0.0556666	−	0.494054i
$236$	−1.85085	+	2.32089i	−0.120480	+	0.151077i
$237$	−2.55375	−	3.09808i	−0.165884	−	0.201242i
$238$	6.35281	−	13.1917i	0.411792	−	0.855094i
$239$	13.4160	−	10.6989i	0.867808	−	0.692053i	−0.0847532	−	0.996402i	$-0.527010\pi$
$239$	13.4160	−	10.6989i	0.867808	−	0.692053i	0.952561	+	0.304349i	$0.0984387\pi$
$240$	10.6793	−	11.0307i	0.689344	−	0.712027i
$241$	15.9674	+	3.64445i	1.02855	+	0.234760i	0.703319	−	0.710875i	$-0.251701\pi$
$241$	15.9674	+	3.64445i	1.02855	+	0.234760i	0.325231	+	0.945634i	$0.394558\pi$
$242$	−16.5274	+	1.86219i	−1.06242	+	0.119706i
$243$	−9.33342	−	12.4855i	−0.598739	−	0.800944i
$244$	−1.97336	+	1.97336i	−0.126332	+	0.126332i
$245$	0.332638	+	1.45738i	0.0212515	+	0.0931088i
$246$	14.6509	+	22.5001i	0.934110	+	1.43455i
$247$	−0.508046	+	0.177773i	−0.0323262	+	0.0113114i
$248$	−15.8454	+	3.61661i	−1.00618	+	0.229655i
$249$	−8.00611	+	13.2116i	−0.507366	+	0.837250i
$250$	−17.9597	−	11.2848i	−1.13587	−	0.713714i
$251$	−2.30792	−	20.4833i	−0.145675	−	1.29290i	−0.827535	−	0.561415i	$-0.810257\pi$
$251$	−2.30792	−	20.4833i	−0.145675	−	1.29290i	0.681860	−	0.731483i	$-0.261171\pi$
$252$	1.97404	+	7.51825i	0.124353	+	0.473605i
$253$	−9.45589	+	5.94153i	−0.594487	+	0.373541i
$254$	−2.84017	−	3.56146i	−0.178208	−	0.223466i
$255$	10.1645	+	2.14751i	0.636523	+	0.134482i
$256$	−17.4954	+	8.42532i	−1.09346	+	0.526582i
$257$	−11.3696	−	9.06698i	−0.709218	−	0.565582i	0.201061	−	0.979579i	$-0.435561\pi$
$257$	−11.3696	−	9.06698i	−0.709218	−	0.565582i	−0.910279	+	0.413996i	$0.864133\pi$
$258$	1.39239	+	10.7858i	0.0866865	+	0.671493i
$259$	−6.62792	+	18.9415i	−0.411839	+	1.17697i
$260$	−2.05207			−0.127264
$261$	−14.5097	+	7.10421i	−0.898125	+	0.439739i
$262$	0.751373			0.0464200
$263$	3.08537	−	8.81747i	0.190252	−	0.543709i	−0.808761	−	0.588138i	$-0.799861\pi$
$263$	3.08537	−	8.81747i	0.190252	−	0.543709i	0.999013	+	0.0444293i	$0.0141469\pi$
$264$	−0.447993	−	3.47025i	−0.0275721	−	0.213579i
$265$	16.2518	+	12.9604i	0.998342	+	0.796151i
$266$	1.89474	−	0.912461i	0.116174	−	0.0559466i
$267$	15.8768	+	3.35439i	0.971645	+	0.205285i
$268$	−7.97114	−	9.99549i	−0.486915	−	0.610572i
$269$	−4.66339	+	2.93020i	−0.284332	+	0.178657i	−0.666645	−	0.745375i	$-0.732270\pi$
$269$	−4.66339	+	2.93020i	−0.284332	+	0.178657i	0.382313	+	0.924033i	$0.375127\pi$
$270$	−14.1310	+	7.67132i	−0.859983	+	0.466862i
$271$	−2.43068	−	21.5728i	−0.147653	−	1.31046i	−0.820914	−	0.571052i	$-0.806536\pi$
$271$	−2.43068	−	21.5728i	−0.147653	−	1.31046i	0.673261	−	0.739405i	$-0.264893\pi$
$272$	−14.3123	−	8.99301i	−0.867810	−	0.545281i
$273$	−2.46812	+	4.07286i	−0.149377	+	0.246501i
$274$	8.82421	−	2.01407i	0.533090	−	0.121674i
$275$	−2.12055	+	0.742012i	−0.127874	+	0.0447450i
$276$	−9.09800	−	13.9722i	−0.547635	−	0.841026i
$277$	−5.43368	−	23.8065i	−0.326478	−	1.43040i	−0.825792	−	0.563974i	$-0.809272\pi$
$277$	−5.43368	−	23.8065i	−0.326478	−	1.43040i	0.499314	−	0.866421i	$-0.333585\pi$
$278$	−7.43820	+	7.43820i	−0.446113	+	0.446113i
$279$	29.1449	+	2.33156i	1.74486	+	0.139587i
$280$	−7.29279	+	0.821700i	−0.435827	+	0.0491060i
$281$	−22.3808	−	5.10828i	−1.33513	−	0.304734i	−0.505392	−	0.862890i	$-0.668652\pi$
$281$	−22.3808	−	5.10828i	−1.33513	−	0.304734i	−0.829737	+	0.558155i	$0.811509\pi$
$282$	9.03330	−	9.33055i	0.537925	−	0.555626i
$283$	−20.7543	+	16.5510i	−1.23372	+	0.983857i	−0.233784	+	0.972288i	$0.575111\pi$
$283$	−20.7543	+	16.5510i	−1.23372	+	0.983857i	−0.999933	+	0.0115684i	$0.996318\pi$
$284$	3.87750	−	8.05171i	0.230087	−	0.477781i
$285$	0.949106	+	1.15141i	0.0562202	+	0.0682035i
$286$	−1.46023	+	1.83107i	−0.0863452	+	0.108273i
$287$	2.46837	−	21.9074i	0.145703	−	1.29315i
$288$	15.9868	−	2.32746i	0.942032	−	0.137147i
$289$			5.56243i			0.327202i
$290$	5.09516	+	15.8658i	0.299198	+	0.931671i
$291$	−8.74780	+	2.14616i	−0.512805	+	0.125810i
$292$	−1.47655	−	0.516668i	−0.0864086	−	0.0302357i
$293$	18.8457	+	2.12340i	1.10098	+	0.124051i	0.643704	−	0.765275i	$-0.277397\pi$
$293$	18.8457	+	2.12340i	1.10098	+	0.124051i	0.457275	+	0.889325i	$0.348826\pi$
$294$	−1.06789	+	2.31251i	−0.0622806	+	0.134868i
$295$	2.18762	+	4.54263i	0.127368	+	0.264482i
$296$	12.1513	+	5.85174i	0.706278	+	0.340125i
$297$	−1.10117	+	6.19752i	−0.0638961	+	0.359617i
$298$	−4.09101	−	6.51081i	−0.236986	−	0.377161i
$299$	2.27308	−	9.95903i	0.131456	−	0.575946i
$300$	−1.15892	−	3.14762i	−0.0669100	−	0.181728i
$301$	4.75084	−	7.56091i	0.273834	−	0.435804i
$302$	10.8971	+	10.8971i	0.627059	+	0.627059i
$303$	−9.43675	−	18.8106i	−0.542127	−	1.08064i
$304$	−0.801856	−	2.29157i	−0.0459896	−	0.131431i
$305$	1.56552	+	4.47401i	0.0896416	+	0.256181i
$306$	11.4792	+	13.4756i	0.656224	+	0.770348i
$307$	1.83383	+	1.83383i	0.104662	+	0.104662i	0.757499	−	0.652837i	$-0.226421\pi$
$307$	1.83383	+	1.83383i	0.104662	+	0.104662i	−0.652837	+	0.757499i	$0.726421\pi$
$308$	1.66992	−	2.65766i	0.0951525	−	0.151434i
$309$	18.4801	−	6.80415i	1.05130	−	0.387074i
$310$	6.71079	−	29.4019i	0.381147	−	1.66991i
$311$	10.6017	+	16.8725i	0.601166	+	0.956750i	0.999224	+	0.0393897i	$0.0125414\pi$
$311$	10.6017	+	16.8725i	0.601166	+	0.956750i	−0.398058	+	0.917360i	$0.630316\pi$
$312$	2.53432	+	1.95479i	0.143477	+	0.110668i
$313$	10.9283	+	5.26280i	0.617705	+	0.297471i	0.716446	−	0.697642i	$-0.245767\pi$
$313$	10.9283	+	5.26280i	0.617705	+	0.297471i	−0.0987415	+	0.995113i	$0.531482\pi$
$314$	7.68581	+	15.9597i	0.433735	+	0.900661i
$315$	12.9596	+	2.51967i	0.730193	+	0.141967i
$316$	−2.40526	−	0.271007i	−0.135306	−	0.0152454i
$317$	19.6625	+	6.88021i	1.10436	+	0.386431i	0.820044	−	0.572301i	$-0.193949\pi$
$317$	19.6625	+	6.88021i	1.10436	+	0.386431i	0.284312	+	0.958732i	$0.408235\pi$
$318$	8.43951	+	34.3997i	0.473264	+	1.92904i
$319$	6.09970	+	2.31310i	0.341518	+	0.129509i
$320$			1.06473i			0.0595204i
$321$	−0.198830	+	2.06447i	−0.0110976	+	0.115227i
$322$	−4.46870	+	39.6608i	−0.249031	+	2.21021i
$323$	1.02426	−	1.28439i	0.0569915	−	0.0714651i
$324$	−9.27826	−	1.49406i	−0.515459	−	0.0830035i
$325$	0.891636	−	1.85150i	0.0494590	−	0.102703i
$326$	−5.55525	+	4.43016i	−0.307677	+	0.245364i
$327$	−13.2024	−	12.7818i	−0.730097	−	0.706837i
$328$	−14.4450	−	3.29698i	−0.797593	−	0.182045i
$329$	−10.5964	+	1.19393i	−0.584198	+	0.0658233i
$330$	6.16221	+	2.04492i	0.339219	+	0.112569i
$331$	12.4740	−	12.4740i	0.685633	−	0.685633i	−0.275630	−	0.961264i	$-0.588887\pi$
$331$	12.4740	−	12.4740i	0.685633	−	0.685633i	0.961264	+	0.275630i	$0.0888866\pi$
$332$	2.07237	+	9.07967i	0.113736	+	0.498311i
$333$	−17.7022	−	16.5917i	−0.970073	−	0.909218i
$334$	33.3844	−	11.6817i	1.82671	−	0.639194i
$335$	−21.1700	+	4.83190i	−1.15664	+	0.263995i
$336$	−18.3709	−	11.1326i	−1.00221	−	0.607333i
$337$	8.26097	+	5.19071i	0.450004	+	0.282756i	0.737906	−	0.674904i	$-0.235815\pi$
$337$	8.26097	+	5.19071i	0.450004	+	0.282756i	−0.287902	+	0.957660i	$0.592958\pi$
$338$	2.29971	+	20.4105i	0.125088	+	1.11018i
$339$	−7.98909	+	0.129318i	−0.433908	+	0.00702359i
$340$	5.30312	−	3.33217i	0.287602	−	0.180712i
$341$	−7.36108	−	9.23050i	−0.398625	−	0.499860i
$342$	0.0822908	+	2.54124i	0.00444977	+	0.137414i
$343$	17.5337	−	8.44379i	0.946732	−	0.455922i
$344$	−4.69203	−	3.74177i	−0.252977	−	0.201743i
$345$	−28.0858	+	3.62574i	−1.51209	+	0.195203i
$346$	1.90499	−	5.44414i	0.102413	−	0.292679i
$347$	13.9768			0.750316			0.375158	−	0.926961i	$-0.377588\pi$
$347$	13.9768			0.750316			0.375158	+	0.926961i	$0.377588\pi$
$348$	−3.30560	+	9.16152i	−0.177199	+	0.491109i
$349$	−15.1394			−0.810391			−0.405196	−	0.914230i	$-0.632797\pi$
$349$	−15.1394			−0.810391			−0.405196	+	0.914230i	$0.632797\pi$
$350$	−2.65186	+	7.57859i	−0.141748	+	0.405093i
$351$	−3.29632	−	4.72078i	−0.175944	−	0.251977i
$352$	−5.10027	−	4.06733i	−0.271846	−	0.216790i
$353$	15.0405	−	7.24310i	0.800522	−	0.385511i	0.0115449	−	0.999933i	$-0.496325\pi$
$353$	15.0405	−	7.24310i	0.800522	−	0.385511i	0.788978	+	0.614422i	$0.210611\pi$
$354$	−1.77592	+	8.40567i	−0.0943889	+	0.446756i
$355$	−9.46378	−	11.8672i	−0.502285	−	0.629846i
$356$	8.28343	−	5.20483i	0.439021	−	0.275855i
$357$	−0.235246	−	14.5331i	−0.0124505	−	0.769176i
$358$	1.08287	+	9.61072i	0.0572314	+	0.507942i
$359$	−4.93936	−	3.10361i	−0.260690	−	0.163802i	0.395346	−	0.918532i	$-0.370625\pi$
$359$	−4.93936	−	3.10361i	−0.260690	−	0.163802i	−0.656035	+	0.754730i	$0.727768\pi$
$360$	2.65794	−	8.46543i	0.140086	−	0.446167i
$361$	−18.2936	+	4.17539i	−0.962821	+	0.219758i
$362$	−12.9810	+	4.54225i	−0.682266	+	0.238735i
$363$	−13.8361	+	9.00940i	−0.726207	+	0.472871i
$364$	0.638870	+	2.79907i	0.0334859	+	0.146711i
$365$	−1.87876	+	1.87876i	−0.0983389	+	0.0983389i
$366$	−2.54384	+	7.66567i	−0.132969	+	0.400691i
$367$	2.23954	−	0.252336i	0.116903	−	0.0131718i	−0.0533190	−	0.998578i	$-0.516980\pi$
$367$	2.23954	−	0.252336i	0.116903	−	0.0131718i	0.170222	+	0.985406i	$0.445551\pi$
$368$	44.9208	+	10.2529i	2.34166	+	0.534469i
$369$	23.0157	+	13.4429i	1.19815	+	0.699811i
$370$	−19.5658	+	15.6032i	−1.01718	+	0.811170i
$371$	12.6186	−	26.2028i	0.655126	−	1.36038i
$372$	13.6014	−	11.2117i	0.705200	−	0.581297i
$373$	−19.9800	+	25.0542i	−1.03453	+	1.29726i	−0.0807529	+	0.996734i	$0.525732\pi$
$373$	−19.9800	+	25.0542i	−1.03453	+	1.29726i	−0.953775	+	0.300522i	$0.902839\pi$
$374$	0.800330	−	7.10313i	0.0413841	−	0.367294i
$375$	−20.9593	−	2.01860i	−1.08233	−	0.104240i
$376$			7.16659i			0.369589i
$377$	−5.44139	+	2.44917i	−0.280246	+	0.126139i
$378$	14.8632	+	16.8867i	0.764483	+	0.868556i
$379$	−9.87263	−	3.45458i	−0.507123	−	0.177450i	0.0645770	−	0.997913i	$-0.479430\pi$
$379$	−9.87263	−	3.45458i	−0.507123	−	0.177450i	−0.571700	+	0.820463i	$0.693716\pi$
$380$	0.893920	+	0.100721i	0.0458571	+	0.00516686i
$381$	−4.10548	−	1.89586i	−0.210330	−	0.0971280i
$382$	7.06218	+	14.6648i	0.361333	+	0.750315i
$383$	11.3746	+	5.47770i	0.581213	+	0.279897i	0.701300	−	0.712866i	$-0.252603\pi$
$383$	11.3746	+	5.47770i	0.581213	+	0.279897i	−0.120087	+	0.992763i	$0.538317\pi$
$384$	−12.5014	+	16.2076i	−0.637961	+	0.827092i
$385$	−2.83630	−	4.51395i	−0.144551	−	0.230052i
$386$	4.60462	−	20.1742i	0.234369	−	1.02684i
$387$	6.03669	+	8.95058i	0.306862	+	0.454983i
$388$	−2.88902	+	4.59785i	−0.146668	+	0.233421i
$389$	−5.76046	−	5.76046i	−0.292067	−	0.292067i	0.545829	−	0.837896i	$-0.316215\pi$
$389$	−5.76046	−	5.76046i	−0.292067	−	0.292067i	−0.837896	+	0.545829i	$0.816215\pi$
$390$	−5.30836	+	2.66306i	−0.268799	+	0.134849i
$391$	10.2973	+	29.4280i	0.520756	+	1.48824i
$392$	−0.464245	−	1.32673i	−0.0234479	−	0.0670102i
$393$	0.666705	−	0.334467i	0.0336308	−	0.0168716i
$394$	5.03164	+	5.03164i	0.253490	+	0.253490i
$395$	−2.18723	+	3.48096i	−0.110052	+	0.175146i
$396$	2.12190	+	3.14613i	0.106629	+	0.158099i
$397$	−3.95989	+	17.3494i	−0.198741	+	0.870743i	0.772946	+	0.634472i	$0.218782\pi$
$397$	−3.95989	+	17.3494i	−0.198741	+	0.870743i	−0.971687	+	0.236271i	$0.924075\pi$
$398$	−10.1860	−	16.2110i	−0.510580	−	0.812583i
$399$	1.27506	−	1.65307i	0.0638330	−	0.0827571i
$400$	8.35131	+	4.02178i	0.417565	+	0.201089i
$401$	−6.89266	−	14.3128i	−0.344203	−	0.714745i	0.654959	−	0.755664i	$-0.272686\pi$
$401$	−6.89266	−	14.3128i	−0.344203	−	0.714745i	−0.999162	+	0.0409190i	$0.986971\pi$
$402$	−33.5916	−	15.5122i	−1.67539	−	0.773677i
$403$	10.7314	+	1.20914i	0.534570	+	0.0602315i
$404$	−11.9754	−	4.19036i	−0.595797	−	0.208478i
$405$	−9.12380	+	13.0972i	−0.453365	+	0.650803i
$406$	20.0550	−	11.8894i	0.995314	−	0.590061i
$407$			9.79700i			0.485619i
$408$	−9.72359	−	0.936484i	−0.481390	−	0.0463629i
$409$	1.02652	−	9.11057i	0.0507579	−	0.450489i	−0.942469	−	0.334295i	$-0.891502\pi$
$409$	1.02652	−	9.11057i	0.0507579	−	0.450489i	0.993227	−	0.116194i	$-0.0370695\pi$
$410$	17.1414	−	21.4947i	0.846555	−	1.06155i
$411$	6.93332	−	5.71514i	0.341995	−	0.281907i
$412$	5.15117	−	10.6965i	0.253780	−	0.526980i
$413$	5.51519	−	4.39822i	0.271385	−	0.216422i
$414$	−41.6673	−	24.3368i	−2.04783	−	1.19609i
$415$	15.4215	+	3.51986i	0.757011	+	0.172783i
$416$	5.92960	−	0.668105i	0.290722	−	0.0327565i
$417$	−3.28898	+	9.91108i	−0.161062	+	0.485348i
$418$	0.725976	−	0.725976i	0.0355087	−	0.0355087i
$419$	−3.95430	−	17.3249i	−0.193180	−	0.846377i	−0.974881	−	0.222724i	$-0.928505\pi$
$419$	−3.95430	−	17.3249i	−0.193180	−	0.846377i	0.781701	−	0.623653i	$-0.214352\pi$
$420$	6.66988	−	4.34310i	0.325457	−	0.211922i
$421$	9.92465	−	3.47278i	0.483698	−	0.169253i	−0.0774043	−	0.997000i	$-0.524663\pi$
$421$	9.92465	−	3.47278i	0.483698	−	0.169253i	0.561102	+	0.827747i	$0.310378\pi$
$422$	42.1519	−	9.62090i	2.05192	−	0.468338i
$423$	3.86197	−	12.3002i	0.187776	−	0.598058i
$424$	−16.5499	−	10.3990i	−0.803735	−	0.505020i
$425$	0.702250	+	6.23264i	0.0340641	+	0.302327i
$426$	−0.418598	−	25.8604i	−0.0202812	−	1.25294i
$427$	5.61526	−	3.52830i	0.271741	−	0.170746i
$428$	0.779588	+	0.977572i	0.0376828	+	0.0472527i
$429$	−0.480600	+	2.27475i	−0.0232036	+	0.109826i
$430$	10.0330	−	4.83162i	0.483832	−	0.233001i
$431$	−11.2015	−	8.93286i	−0.539555	−	0.430281i	0.315418	−	0.948953i	$-0.397855\pi$
$431$	−11.2015	−	8.93286i	−0.539555	−	0.430281i	−0.854973	+	0.518672i	$0.826427\pi$
$432$	21.2934	−	14.8682i	1.02448	−	0.715349i
$433$	3.24108	−	9.26247i	0.155756	−	0.445126i	−0.839390	−	0.543529i	$-0.817088\pi$
$433$	3.24108	−	9.26247i	0.155756	−	0.445126i	0.995147	+	0.0984033i	$0.0313735\pi$
$434$	−42.1941			−2.02538
$435$	11.5835	+	11.8099i	0.555388	+	0.566241i
$436$	−11.0783			−0.530557
$437$	−1.47901	+	4.22677i	−0.0707507	+	0.202194i
$438$	−4.49009	+	0.579649i	−0.214545	+	0.0276967i
$439$	−30.2976	−	24.1616i	−1.44603	−	1.15317i	−0.960269	−	0.279075i	$-0.909972\pi$
$439$	−30.2976	−	24.1616i	−1.44603	−	1.15317i	−0.485758	−	0.874093i	$-0.661456\pi$
$440$	−3.22804	+	1.55454i	−0.153891	+	0.0741099i
$441$	0.0818391	+	2.52729i	0.00389710	+	0.120347i
$442$	4.07664	+	5.11195i	0.193906	+	0.243150i
$443$	−16.3625	+	10.2813i	−0.777408	+	0.488478i	−0.861362	−	0.507992i	$-0.830388\pi$
$443$	−16.3625	+	10.2813i	−0.777408	+	0.488478i	0.0839538	+	0.996470i	$0.473245\pi$
$444$	−14.6249	+	0.236732i	−0.694069	+	0.0112348i
$445$	−1.86040	−	16.5115i	−0.0881912	−	0.782718i
$446$	27.0834	+	17.0176i	1.28244	+	0.805808i
$447$	−6.52826	−	3.95607i	−0.308776	−	0.187116i
$448$	1.45232	−	0.331483i	0.0686158	−	0.0156611i
$449$	−0.404176	+	0.141427i	−0.0190742	+	0.00667436i	−0.339799	−	0.940498i	$-0.610359\pi$
$449$	−0.404176	+	0.141427i	−0.0190742	+	0.00667436i	0.320725	+	0.947172i	$0.396073\pi$
$450$	−7.08272	−	6.63840i	−0.333883	−	0.312937i
$451$	−2.39496	−	10.4930i	−0.112774	−	0.494096i
$452$	−3.40613	+	3.40613i	−0.160211	+	0.160211i
$453$	14.5200	+	4.81843i	0.682207	+	0.226390i
$454$	42.0924	−	4.74268i	1.97549	−	0.222585i
$455$	4.75413	+	1.08510i	0.222877	+	0.0508702i
$456$	−1.00805	−	0.975935i	−0.0472062	−	0.0457023i
$457$	−6.74257	+	5.37702i	−0.315404	+	0.251526i	−0.768376	−	0.639998i	$-0.778935\pi$
$457$	−6.74257	+	5.37702i	−0.315404	+	0.251526i	0.452972	+	0.891525i	$0.350364\pi$
$458$	−4.67674	+	9.71134i	−0.218530	+	0.453781i
$459$	16.1843	+	6.84722i	0.755416	+	0.319601i
$460$	−10.6445	+	13.3478i	−0.496305	+	0.622346i
$461$	−3.41255	+	30.2872i	−0.158938	+	1.41062i	0.620534	+	0.784180i	$0.286916\pi$
$461$	−3.41255	+	30.2872i	−0.158938	+	1.41062i	−0.779472	+	0.626437i	$0.784512\pi$
$462$	0.870844	−	9.04205i	0.0405153	−	0.420674i
$463$		−	18.6575i		−	0.867086i	−0.901133	−	0.433543i	$-0.857263\pi$
$463$		−	18.6575i		−	0.867086i	0.901133	−	0.433543i	$-0.142737\pi$
$464$	−11.0471	−	24.5437i	−0.512851	−	1.13941i
$465$	−7.13342	−	29.0760i	−0.330804	−	1.34837i
$466$	22.3411	+	7.81750i	1.03493	+	0.362139i
$467$	−18.2564	−	2.05701i	−0.844807	−	0.0951869i	−0.321058	−	0.947060i	$-0.604038\pi$
$467$	−18.2564	−	2.05701i	−0.844807	−	0.0951869i	−0.523749	+	0.851873i	$0.675467\pi$
$468$	−3.40735	−	0.662472i	−0.157505	−	0.0306228i
$469$	13.1817	+	27.3720i	0.608673	+	1.26392i
$470$	−11.9810	−	5.76976i	−0.552644	−	0.266139i
$471$	13.9241	+	10.7401i	0.641588	+	0.494876i
$472$	−2.52232	−	4.01425i	−0.116099	−	0.184771i
$473$	0.970062	−	4.25012i	0.0446035	−	0.195421i
$474$	−6.57369	+	2.42035i	−0.301940	+	0.111170i
$475$	−0.479289	+	0.762784i	−0.0219913	+	0.0349989i
$476$	−6.19618	−	6.19618i	−0.284001	−	0.284001i
$477$	22.8013	+	26.7666i	1.04400	+	1.22556i
$478$	−9.88842	−	28.2595i	−0.452286	−	1.29256i
$479$	4.21591	+	12.0484i	0.192630	+	0.550504i	0.999173	−	0.0406714i	$-0.0129497\pi$
$479$	4.21591	+	12.0484i	0.192630	+	0.550504i	−0.806543	+	0.591176i	$0.798664\pi$
$480$	−7.41770	−	14.7860i	−0.338570	−	0.674883i
$481$	−6.33668	−	6.33668i	−0.288928	−	0.288928i
$482$	15.2032	−	24.1958i	0.692488	−	1.10209i
$483$	13.6895	+	37.1809i	0.622895	+	1.69179i
$484$	−2.21494	+	9.70428i	−0.100679	+	0.441104i
$485$	4.90690	+	7.80929i	0.222811	+	0.354602i
$486$	−25.9402	+	8.17590i	−1.17667	+	0.370866i
$487$	−11.2965	−	5.44009i	−0.511892	−	0.246514i	0.160062	−	0.987107i	$-0.448831\pi$
$487$	−11.2965	−	5.44009i	−0.511892	−	0.246514i	−0.671954	+	0.740593i	$0.734545\pi$
$488$	−1.93382	−	4.01562i	−0.0875400	−	0.181779i
$489$	−2.95721	+	6.40383i	−0.133730	+	0.289591i
$490$	2.59178	+	0.292024i	0.117085	+	0.0131923i
$491$	15.4772	+	5.41572i	0.698477	+	0.244408i	0.656078	−	0.754693i	$-0.272214\pi$
$491$	15.4772	+	5.41572i	0.698477	+	0.244408i	0.0423993	+	0.999101i	$0.486500\pi$
$492$	15.6061	−	3.82874i	0.703576	−	0.172613i
$493$	10.0851	−	15.1651i	0.454209	−	0.683003i
$494$			0.939121i			0.0422530i
$495$	6.37811	−	0.928565i	0.286675	−	0.0417359i
$496$	−5.45390	+	48.4047i	−0.244887	+	2.17343i
$497$	−13.2408	+	16.6034i	−0.593931	+	0.744765i
$498$	17.1439	+	20.7982i	0.768239	+	0.931988i
$499$	8.87570	−	18.4306i	0.397331	−	0.825066i	−0.602310	−	0.798262i	$-0.705753\pi$
$499$	8.87570	−	18.4306i	0.397331	−	0.825066i	0.999641	−	0.0268037i	$-0.00853291\pi$
$500$	−9.92468	+	7.91467i	−0.443845	+	0.353955i
$501$	24.4225	−	25.2261i	1.09112	−	1.12702i
$502$	−35.0630	−	8.00291i	−1.56494	−	0.357187i
$503$	−0.689827	+	0.0777249i	−0.0307579	+	0.00346558i	−0.127330	−	0.991860i	$-0.540641\pi$
$503$	−0.689827	+	0.0777249i	−0.0307579	+	0.00346558i	0.0965721	+	0.995326i	$0.469212\pi$
$504$	−12.3745	−	0.989950i	−0.551206	−	0.0440959i
$505$	−15.2374	+	15.2374i	−0.678057	+	0.678057i
$506$	4.33579	+	18.9963i	0.192749	+	0.844490i
$507$	11.1261	+	17.0869i	0.494129	+	0.758854i
$508$	−2.57324	+	0.900415i	−0.114169	+	0.0399495i
$509$	14.3369	−	3.27230i	0.635471	−	0.145042i	0.107364	−	0.994220i	$-0.465759\pi$
$509$	14.3369	−	3.27230i	0.635471	−	0.145042i	0.528107	+	0.849178i	$0.322902\pi$
$510$	9.39399	−	15.5019i	0.415973	−	0.686434i
$511$	3.14759	+	1.97776i	0.139241	+	0.0874910i
$512$	1.14709	+	10.1807i	0.0506945	+	0.449926i
$513$	1.20423	+	2.21825i	0.0531680	+	0.0979382i
$514$	−21.4838	+	13.4992i	−0.947611	+	0.595423i
$515$	−12.5724	−	15.7653i	−0.554007	−	0.694702i
$516$	6.36801	+	1.34541i	0.280336	+	0.0592283i
$517$	−4.69033	+	2.25875i	−0.206281	+	0.0993395i
$518$	27.3745	+	21.8304i	1.20277	+	0.959174i
$519$	−0.733088	−	5.67866i	−0.0321790	−	0.249266i
$520$	1.08242	−	3.09337i	0.0474671	−	0.135653i
$521$	10.8298			0.474462			0.237231	−	0.971453i	$-0.423760\pi$
$521$	10.8298			0.474462			0.237231	+	0.971453i	$0.423760\pi$
$522$	3.33826	+	27.9891i	0.146112	+	1.22505i
$523$	5.85546			0.256041			0.128021	−	0.991771i	$-0.459138\pi$
$523$	5.85546			0.256041			0.128021	+	0.991771i	$0.459138\pi$
$524$	0.148519	−	0.424444i	0.00648810	−	0.0185419i
$525$	1.02051	+	7.90506i	0.0445385	+	0.345005i
$526$	−12.7431	−	10.1623i	−0.555626	−	0.443097i
$527$	−29.6964	+	14.3010i	−1.29359	+	0.622962i
$528$	−10.2604	−	2.16777i	−0.446526	−	0.0943403i
$529$	−38.6480	−	48.4630i	−1.68035	−	2.10709i
$530$	30.7091	−	19.2958i	1.33392	−	0.838157i
$531$	2.16591	+	8.24902i	0.0939927	+	0.357977i
$532$	−0.140918	−	1.25069i	−0.00610959	−	0.0542241i
$533$	8.33591	+	5.23780i	0.361068	+	0.226874i
$534$	14.6733	−	24.2138i	0.634977	−	1.04783i
$535$	2.07045	−	0.472567i	0.0895134	−	0.0204308i
$536$	19.2722	−	6.74362i	0.832430	−	0.291280i
$537$	5.23898	+	8.04572i	0.226079	+	0.347198i
$538$	2.13829	+	9.36846i	0.0921883	+	0.403903i
$539$	0.721992	−	0.721992i	0.0310984	−	0.0310984i
$540$	1.54028	+	9.49880i	0.0662831	+	0.408763i
$541$	27.5408	−	3.10311i	1.18407	−	0.133413i	0.502112	−	0.864802i	$-0.332556\pi$
$541$	27.5408	−	3.10311i	1.18407	−	0.133413i	0.681960	+	0.731389i	$0.261128\pi$
$542$	−36.9280	−	8.42857i	−1.58619	−	0.362038i
$543$	−9.49631	+	9.80880i	−0.407526	+	0.420936i
$544$	−14.2388	+	11.3551i	−0.610486	+	0.486846i
$545$	−8.16404	+	16.9528i	−0.349709	+	0.726178i
$546$	5.28512	+	6.41165i	0.226182	+	0.274393i
$547$	−18.6234	+	23.3530i	−0.796278	+	0.998502i	0.203533	+	0.979068i	$0.434758\pi$
$547$	−18.6234	+	23.3530i	−0.796278	+	0.998502i	−0.999811	+	0.0194334i	$0.993814\pi$
$548$	0.606499	−	5.38283i	0.0259084	−	0.229943i
$549$	1.15512	+	7.93424i	0.0492992	+	0.338625i
$550$			3.91982i			0.167142i
$551$	2.49058	−	0.799828i	0.106102	−	0.0340738i
$552$	25.8612	−	6.34469i	1.10072	−	0.270048i
$553$	5.42907	+	1.89971i	0.230867	+	0.0807840i
$554$	−42.3370	−	4.77024i	−1.79873	−	0.202668i
$555$	−10.4154	+	22.5545i	−0.442109	+	0.957384i
$556$	2.73151	+	5.67204i	0.115842	+	0.240548i
$557$	−20.5785	−	9.91006i	−0.871937	−	0.419903i	−0.0562642	−	0.998416i	$-0.517919\pi$
$557$	−20.5785	−	9.91006i	−0.871937	−	0.419903i	−0.815673	+	0.578513i	$0.803633\pi$
$558$	20.6347	−	46.6538i	0.873538	−	1.97501i
$559$	2.12154	+	3.37641i	0.0897315	+	0.142807i
$560$	−4.89441	+	21.4438i	−0.206826	+	0.906166i
$561$	−2.45175	−	6.65898i	−0.103513	−	0.281142i
$562$	−21.3097	+	33.9143i	−0.898897	+	1.43059i
$563$	10.4785	+	10.4785i	0.441617	+	0.441617i	0.892555	−	0.450938i	$-0.148911\pi$
$563$	10.4785	+	10.4785i	0.441617	+	0.441617i	−0.450938	+	0.892555i	$0.648911\pi$
$564$	−3.48519	−	6.94714i	−0.146753	−	0.292528i
$565$	2.70218	+	7.72239i	0.113682	+	0.324883i
$566$	15.2972	+	43.7170i	0.642991	+	1.83756i
$567$	20.7053	+	8.36755i	0.869543	+	0.351404i
$568$	10.0922	+	10.0922i	0.423458	+	0.423458i
$569$	−19.8489	+	31.5893i	−0.832107	+	1.32429i	0.111682	+	0.993744i	$0.464376\pi$
$569$	−19.8489	+	31.5893i	−0.832107	+	1.32429i	−0.943789	+	0.330547i	$0.892767\pi$
$570$	2.44313	−	0.899530i	0.102331	−	0.0376772i
$571$	4.57150	−	20.0290i	0.191311	−	0.838189i	−0.784597	−	0.620007i	$-0.787130\pi$
$571$	4.57150	−	20.0290i	0.191311	−	0.838189i	0.975908	−	0.218183i	$-0.0700129\pi$
$572$	0.745721	+	1.18681i	0.0311801	+	0.0496229i
$573$	12.7943	+	9.86862i	0.534489	+	0.412267i
$574$	−34.6559	−	16.6894i	−1.44651	−	0.696602i
$575$	−7.41810	−	15.4038i	−0.309356	−	0.642385i
$576$	−0.343729	+	1.76793i	−0.0143220	+	0.0736638i
$577$	47.2544	+	5.32429i	1.96723	+	0.221653i	0.999535	−	0.0304845i	$-0.00970503\pi$
$577$	47.2544	+	5.32429i	1.96723	+	0.221653i	0.967691	+	0.252138i	$0.0811336\pi$
$578$	9.16050	+	3.20540i	0.381027	+	0.133327i
$579$	−4.89461	−	19.9506i	−0.203413	−	0.829118i
$580$	9.96957	+	0.257885i	0.413964	+	0.0107081i
$581$		−	22.1311i		−	0.918154i
$582$	−1.50659	+	15.6431i	−0.0624502	+	0.648426i
$583$	1.58970	−	14.1090i	0.0658387	−	0.584334i
$584$	1.55769	−	1.95328i	0.0644576	−	0.0808273i
$585$	−3.52476	+	4.72595i	−0.145731	+	0.195394i
$586$	14.3569	−	29.8125i	0.593080	−	1.23154i
$587$	−14.0552	+	11.2086i	−0.580119	+	0.462629i	−0.869053	−	0.494720i	$-0.835271\pi$
$587$	−14.0552	+	11.2086i	−0.580119	+	0.462629i	0.288934	+	0.957349i	$0.406699\pi$
$588$	1.09523	+	1.06034i	0.0451667	+	0.0437278i
$589$	−4.61545	−	1.05345i	−0.190176	−	0.0434065i
$590$	8.74168	−	0.984951i	0.359889	−	0.0405498i
$591$	6.70444	+	2.22486i	0.275784	+	0.0915186i
$592$	28.5820	−	28.5820i	1.17471	−	1.17471i
$593$	−7.33679	−	32.1446i	−0.301286	−	1.32002i	−0.868189	−	0.496234i	$-0.834716\pi$
$593$	−7.33679	−	32.1446i	−0.301286	−	1.32002i	0.566903	−	0.823785i	$-0.308141\pi$
$594$	9.57185	+	5.38484i	0.392738	+	0.220942i
$595$	−14.0480	+	4.91560i	−0.575911	+	0.201520i
$596$	−4.48655	+	1.02403i	−0.183776	+	0.0419457i
$597$	−16.2544	−	9.85004i	−0.665249	−	0.403135i
$598$	−15.0912	−	9.48242i	−0.617124	−	0.387765i
$599$	−0.0259349	−	0.230179i	−0.00105967	−	0.00940485i	0.993171	−	0.116666i	$-0.0372206\pi$
$599$	−0.0259349	−	0.230179i	−0.00105967	−	0.00940485i	−0.994231	+	0.107261i	$0.965792\pi$
$600$	5.35614	−	0.0866990i	0.218664	−	0.00353947i
$601$	5.17627	−	3.25247i	0.211144	−	0.132671i	−0.422308	−	0.906452i	$-0.638780\pi$
$601$	5.17627	−	3.25247i	0.211144	−	0.132671i	0.633453	+	0.773781i	$0.281637\pi$
$602$	−9.71400	−	12.1810i	−0.395913	−	0.496459i
$603$	−36.7114	+	1.18880i	−1.49501	+	0.0484115i
$604$	8.30966	−	4.00172i	0.338115	−	0.162828i
$605$	13.2178	+	10.5409i	0.537382	+	0.428548i
$606$	−36.4163	+	4.70117i	−1.47931	+	0.190972i
$607$	−4.49999	+	12.8602i	−0.182649	+	0.521981i	−0.998408	−	0.0564117i	$-0.982034\pi$
$607$	−4.49999	+	12.8602i	−0.182649	+	0.521981i	0.815759	+	0.578393i	$0.196320\pi$
$608$	−2.61583			−0.106086
$609$	12.5027	−	19.4770i	0.506634	−	0.789247i
$610$	8.27018			0.334850
$611$	1.57275	−	4.49465i	0.0636266	−	0.181834i
$612$	9.88127	−	3.82088i	0.399427	−	0.154450i
$613$	21.5711	+	17.2023i	0.871247	+	0.694796i	0.953363	−	0.301826i	$-0.0975963\pi$
$613$	21.5711	+	17.2023i	0.871247	+	0.694796i	−0.0821159	+	0.996623i	$0.526168\pi$
$614$	4.07681	−	1.96329i	0.164527	−	0.0792319i
$615$	5.64169	−	26.7029i	0.227495	−	1.07677i
$616$	3.12542	+	3.91915i	0.125927	+	0.157907i
$617$	12.3887	−	7.78436i	0.498752	−	0.313387i	−0.259058	−	0.965862i	$-0.583412\pi$
$617$	12.3887	−	7.78436i	0.498752	−	0.313387i	0.757810	+	0.652475i	$0.226269\pi$
$618$	−0.556098	−	34.3550i	−0.0223696	−	1.38196i
$619$	1.50822	+	13.3858i	0.0606205	+	0.538022i	0.986917	+	0.161227i	$0.0515451\pi$
$619$	1.50822	+	13.3858i	0.0606205	+	0.538022i	−0.926297	+	0.376794i	$0.877026\pi$
$620$	−15.2824	−	9.60256i	−0.613756	−	0.385648i
$621$	−47.8054	−	3.04662i	−1.91836	−	0.122256i
$622$	33.8958	−	7.73649i	1.35910	−	0.310205i
$623$	−21.9428	+	7.67813i	−0.879121	+	0.307618i
$624$	8.03852	−	5.23429i	0.321798	−	0.209539i
$625$	2.73427	+	11.9796i	0.109371	+	0.479184i
$626$	14.9646	−	14.9646i	0.598105	−	0.598105i
$627$	0.321008	−	0.967333i	0.0128198	−	0.0386315i
$628$	10.5347	−	1.18698i	0.420381	−	0.0473656i
$629$	26.6653	+	6.08619i	1.06322	+	0.242672i
$630$	11.6176	−	19.8906i	0.462858	−	0.792462i
$631$	−16.5679	+	13.2125i	−0.659558	+	0.525980i	−0.895089	−	0.445887i	$-0.852888\pi$
$631$	−16.5679	+	13.2125i	−0.659558	+	0.525980i	0.235531	+	0.971867i	$0.424317\pi$
$632$	1.67724	−	3.48283i	0.0667170	−	0.138539i
$633$	33.1194	−	27.3004i	1.31638	−	1.08509i
$634$	22.6614	−	28.4165i	0.899998	−	1.12856i
$635$	−0.518440	+	4.60128i	−0.0205737	+	0.182596i
$636$	21.1003	+	2.03218i	0.836681	+	0.0805811i
$637$			0.933967i			0.0370051i
$638$	7.32434	−	8.71237i	0.289973	−	0.344926i
$639$	−11.8830	−	22.7600i	−0.470084	−	0.900373i
$640$	19.7829	+	6.92234i	0.781989	+	0.273630i
$641$	−33.9080	−	3.82051i	−1.33929	−	0.150901i	−0.586919	−	0.809646i	$-0.699659\pi$
$641$	−33.9080	−	3.82051i	−1.33929	−	0.150901i	−0.752367	+	0.658745i	$0.771088\pi$
$642$	3.28530	+	1.51711i	0.129660	+	0.0598756i
$643$	−8.94126	−	18.5667i	−0.352609	−	0.732200i	0.646931	−	0.762549i	$-0.276052\pi$
$643$	−8.94126	−	18.5667i	−0.352609	−	0.732200i	−0.999539	+	0.0303492i	$0.990338\pi$
$644$	21.5207	+	10.3638i	0.848036	+	0.408392i
$645$	6.75165	−	8.75326i	0.265846	−	0.344659i
$646$	−1.52495	−	2.42695i	−0.0599985	−	0.0954870i
$647$	−8.36804	+	36.6628i	−0.328982	+	1.44136i	0.492093	+	0.870543i	$0.336232\pi$
$647$	−8.36804	+	36.6628i	−0.328982	+	1.44136i	−0.821075	+	0.570821i	$0.806625\pi$
$648$	7.14626	−	13.1983i	0.280732	−	0.518479i
$649$	1.83224	−	2.91599i	0.0719216	−	0.114463i
$650$	−2.53534	−	2.53534i	−0.0994441	−	0.0994441i
$651$	−37.4395	+	18.7824i	−1.46737	+	0.736139i
$652$	1.40449	+	4.01380i	0.0550040	+	0.157192i
$653$	−12.3466	−	35.2847i	−0.483161	−	1.38080i	−0.885216	−	0.465180i	$-0.845990\pi$
$653$	−12.3466	−	35.2847i	−0.483161	−	1.38080i	0.402055	−	0.915616i	$-0.368296\pi$
$654$	−28.6578	+	14.3768i	−1.12061	+	0.562179i
$655$	−0.540062	−	0.540062i	−0.0211020	−	0.0211020i
$656$	−23.6254	+	37.5996i	−0.922418	+	1.46802i
$657$	−3.72610	+	2.51306i	−0.145369	+	0.0980438i
$658$	−4.14004	+	18.1387i	−0.161396	+	0.707121i
$659$	−27.0994	−	43.1284i	−1.05564	−	1.68005i	−0.634140	−	0.773218i	$-0.718646\pi$
$659$	−27.0994	−	43.1284i	−1.05564	−	1.68005i	−0.421502	−	0.906827i	$-0.638497\pi$
$660$	2.37321	−	3.07677i	0.0923770	−	0.119763i
$661$	7.29040	+	3.51087i	0.283564	+	0.136557i	0.570259	−	0.821465i	$-0.306843\pi$
$661$	7.29040	+	3.51087i	0.283564	+	0.136557i	−0.286696	+	0.958022i	$0.592557\pi$
$662$	−13.3546	−	27.7311i	−0.519041	−	1.07780i
$663$	5.89281	+	2.72123i	0.228858	+	0.105684i
$664$	−14.7802	−	1.66532i	−0.573581	−	0.0646271i
$665$	−2.01773	−	0.706033i	−0.0782441	−	0.0273788i
$666$	−37.5251	+	19.5918i	−1.45407	+	0.759166i
$667$	−12.2949	+	48.0983i	−0.476060	+	1.86237i
$668$		−	21.1676i		−	0.818999i
$669$	31.6068	+	3.04406i	1.22199	+	0.117690i
$670$	−4.24194	+	37.6482i	−0.163880	+	1.45448i
$671$	2.01862	−	2.53126i	0.0779278	−	0.0977184i
$672$	−17.8590	+	14.7212i	−0.688928	+	0.567884i
$673$	−4.56760	+	9.48471i	−0.176068	+	0.365609i	−0.970263	−	0.242055i	$-0.922179\pi$
$673$	−4.56760	+	9.48471i	−0.176068	+	0.365609i	0.794195	+	0.607663i	$0.207893\pi$
$674$	13.3088	−	10.6134i	0.512636	−	0.408813i
$675$	−9.23964	−	2.73755i	−0.355634	−	0.105368i
$676$	11.9843	+	2.73533i	0.460934	+	0.105205i
$677$	23.0750	−	2.59993i	0.886846	−	0.0999235i	0.343224	−	0.939254i	$-0.388481\pi$
$677$	23.0750	−	2.59993i	0.886846	−	0.0999235i	0.543622	+	0.839330i	$0.317053\pi$
$678$	−4.39082	+	13.2314i	−0.168628	+	0.508148i
$679$	9.12439	−	9.12439i	0.350162	−	0.350162i
$680$	2.22578	+	9.75177i	0.0853546	+	0.373963i
$681$	35.2381	−	22.9453i	1.35033	−	0.879267i
$682$	−19.4432	+	6.80346i	−0.744517	+	0.260518i
$683$	14.9652	−	3.41570i	0.572627	−	0.130698i	0.0736044	−	0.997288i	$-0.476550\pi$
$683$	14.9652	−	3.41570i	0.572627	−	0.130698i	0.499022	+	0.866589i	$0.333693\pi$
$684$	1.45179	+	0.455826i	0.0555106	+	0.0174289i
$685$	−7.79020	−	4.89491i	−0.297648	−	0.187025i
$686$	−3.80173	−	33.7413i	−0.145151	−	1.28825i
$687$	0.173180	+	10.6988i	0.00660724	+	0.408186i
$688$	−15.2295	+	9.56932i	−0.580619	+	0.364827i
$689$	8.09745	+	10.1539i	0.308488	+	0.386832i
$690$	−10.2136	+	48.3425i	−0.388826	+	1.84037i
$691$	14.5662	−	7.01469i	0.554123	−	0.266852i	−0.135798	−	0.990737i	$-0.543360\pi$
$691$	14.5662	−	7.01469i	0.554123	−	0.266852i	0.689921	+	0.723885i	$0.257645\pi$
$692$	−2.69880	−	2.15222i	−0.102593	−	0.0818152i
$693$	−3.25228	−	8.41081i	−0.123544	−	0.319500i
$694$	8.05427	−	23.0178i	0.305736	−	0.873744i
$695$	10.6927			0.405596
$696$	−12.0668	−	9.81546i	−0.457391	−	0.372054i
$697$	−30.0475			−1.13813
$698$	−8.72419	+	24.9323i	−0.330215	+	0.943701i
$699$	23.3035	−	3.00838i	0.881421	−	0.113787i
$700$	3.75690	+	2.99603i	0.141998	+	0.113239i
$701$	−28.6080	+	13.7769i	−1.08051	+	0.520346i	−0.887479	−	0.460847i	$-0.847546\pi$
$701$	−28.6080	+	13.7769i	−1.08051	+	0.520346i	−0.193029	+	0.981193i	$0.561831\pi$
$702$	−9.67397	+	2.70816i	−0.365120	+	0.102213i
$703$	2.44936	+	3.07140i	0.0923792	+	0.115840i
$704$	0.615785	−	0.386923i	0.0232083	−	0.0145827i
$705$	−13.1993	+	0.213655i	−0.497115	+	0.00804672i
$706$	−3.26113	−	28.9433i	−0.122734	−	1.08930i
$707$	25.5281	+	16.0404i	0.960083	+	0.603260i
$708$	4.39726	+	2.66470i	0.165259	+	0.100146i
$709$	0.0799658	−	0.0182517i	0.00300318	−	0.000685456i	−0.221019	−	0.975269i	$-0.570938\pi$
$709$	0.0799658	−	0.0182517i	0.00300318	−	0.000685456i	0.224022	+	0.974584i	$0.428081\pi$
$710$	−24.9971	+	8.74687i	−0.938125	+	0.328264i
$711$	−4.75555	+	5.07384i	−0.178347	+	0.190284i
$712$	3.47664	+	15.2322i	0.130293	+	0.570850i
$713$	63.5311	−	63.5311i	2.37926	−	2.37926i
$714$	−24.0695	−	7.98744i	−0.900779	−	0.298922i
$715$	2.36568	−	0.266548i	0.0884713	−	0.00996832i
$716$	5.64306	+	1.28799i	0.210891	+	0.0481345i
$717$	−21.3536	−	20.6733i	−0.797466	−	0.772060i
$718$	−7.95753	+	6.34592i	−0.296973	+	0.236828i
$719$	−6.89173	+	14.3108i	−0.257018	+	0.533704i	−0.989053	−	0.147564i	$-0.952857\pi$
$719$	−6.89173	+	14.3108i	−0.257018	+	0.533704i	0.732034	+	0.681268i	$0.238571\pi$
$720$	−21.3167	−	15.8986i	−0.794426	−	0.592507i
$721$	−17.5901	+	22.0573i	−0.655089	+	0.821456i
$722$	−3.66558	+	32.5330i	−0.136419	+	1.21075i
$723$	2.71951	−	28.2369i	0.101140	−	1.05014i
$724$			8.23069i			0.305891i
$725$	−4.56451	+	8.88309i	−0.169522	+	0.329910i
$726$	6.86397	+	27.9778i	0.254746	+	1.03835i
$727$	−4.29705	−	1.50360i	−0.159369	−	0.0557655i	0.249416	−	0.968397i	$-0.419761\pi$
$727$	−4.29705	−	1.50360i	−0.159369	−	0.0557655i	−0.408784	+	0.912631i	$0.634047\pi$
$728$	−4.55642	−	0.513385i	−0.168872	−	0.0190273i
$729$	−19.3777	+	18.8017i	−0.717694	+	0.696358i
$730$	2.01139	+	4.17670i	0.0744450	+	0.154587i
$731$	−10.9653	−	5.28060i	−0.405566	−	0.195310i
$732$	3.82745	+	2.95222i	0.141466	+	0.109117i
$733$	−9.11220	−	14.5020i	−0.336567	−	0.535643i	0.634968	−	0.772538i	$-0.281013\pi$
$733$	−9.11220	−	14.5020i	−0.336567	−	0.535643i	−0.971535	+	0.236895i	$0.923870\pi$
$734$	0.874997	−	3.83361i	0.0322967	−	0.141501i
$735$	2.42972	−	0.894593i	0.0896216	−	0.0329976i
$736$	26.4124	−	42.0351i	0.973574	−	1.54943i
$737$	10.4877	+	10.4877i	0.386318	+	0.386318i
$738$	35.4015	−	30.1569i	1.30315	−	1.11009i
$739$	4.94780	+	14.1400i	0.182008	+	0.520148i	0.998350	−	0.0574202i	$-0.0182875\pi$
$739$	4.94780	+	14.1400i	0.182008	+	0.520148i	−0.816342	+	0.577568i	$0.804002\pi$
$740$	4.94665	+	14.1367i	0.181842	+	0.519676i
$741$	0.418042	+	0.833297i	0.0153572	+	0.0306119i
$742$	−35.8806	−	35.8806i	−1.31722	−	1.31722i
$743$	−5.32655	+	8.47716i	−0.195412	+	0.310997i	−0.930029	−	0.367485i	$-0.880219\pi$
$743$	−5.32655	+	8.47716i	−0.195412	+	0.310997i	0.734617	+	0.678482i	$0.237362\pi$
$744$	9.72646	+	26.4171i	0.356589	+	0.968500i
$745$	−1.73927	+	7.62024i	−0.0637220	+	0.279184i
$746$	29.7469	+	47.3419i	1.08911	+	1.73331i
$747$	24.4702	+	10.8231i	0.895319	+	0.395995i
$748$	−3.85430	−	1.85613i	−0.140927	−	0.0678669i
$749$	−1.28918	−	2.67702i	−0.0471058	−	0.0978162i
$750$	−15.4023	+	33.3536i	−0.562412	+	1.21790i
$751$	−0.260316	−	0.0293306i	−0.00949907	−	0.00107029i	0.107214	−	0.994236i	$-0.465807\pi$
$751$	−0.260316	−	0.0293306i	−0.00949907	−	0.00107029i	−0.116713	+	0.993166i	$0.537236\pi$
$752$	20.2734	+	7.09398i	0.739295	+	0.258691i
$753$	−34.6744	+	8.50691i	−1.26361	+	0.310009i
$754$	0.897778	+	10.3725i	0.0326951	+	0.377745i
$755$		−	15.6650i		−	0.570107i
$756$	12.4771	−	5.05823i	0.453786	−	0.183966i
$757$	4.38898	−	38.9533i	0.159520	−	1.41578i	−0.617631	−	0.786468i	$-0.711907\pi$
$757$	4.38898	−	38.9533i	0.159520	−	1.41578i	0.777151	−	0.629314i	$-0.216664\pi$
$758$	−11.3784	+	14.2680i	−0.413281	+	0.518239i
$759$	12.3033	+	14.9257i	0.446580	+	0.541769i
$760$	−0.623351	+	1.29440i	−0.0226113	+	0.0469529i
$761$	18.6302	−	14.8571i	0.675344	−	0.538569i	−0.224667	−	0.974436i	$-0.572129\pi$
$761$	18.6302	−	14.8571i	0.675344	−	0.538569i	0.900011	+	0.435867i	$0.143558\pi$
$762$	−5.48803	+	5.66862i	−0.198810	+	0.205352i
$763$	25.6657	+	5.85803i	0.929161	+	0.212075i
$764$	9.67994	−	1.09067i	0.350208	−	0.0394590i
$765$	1.43492	−	17.9367i	0.0518795	−	0.648503i
$766$	15.5757	−	15.5757i	0.562771	−	0.562771i
$767$	0.700969	+	3.07114i	0.0253105	+	0.110893i
$768$	18.3527	+	28.1851i	0.662247	+	1.01704i
$769$	−2.11272	+	0.739272i	−0.0761865	+	0.0266588i	−0.368103	−	0.929785i	$-0.619993\pi$
$769$	−2.11272	+	0.739272i	−0.0761865	+	0.0266588i	0.291917	+	0.956444i	$0.405707\pi$
$770$	−9.06825	+	2.06977i	−0.326797	+	0.0745893i
$771$	−13.0539	+	21.5414i	−0.470125	+	0.775794i
$772$	−10.4860	−	6.58882i	−0.377401	−	0.237137i
$773$	0.614691	+	5.45554i	0.0221089	+	0.196222i	0.999911	−	0.0133064i	$-0.00423568\pi$
$773$	0.614691	+	5.45554i	0.0221089	+	0.196222i	−0.977803	+	0.209528i	$0.932807\pi$
$774$	18.2190	−	4.78369i	0.654868	−	0.171946i
$775$	15.3043	−	9.61632i	0.549746	−	0.345428i
$776$	−5.40709	−	6.78027i	−0.194103	−	0.243398i
$777$	34.0075	+	7.18496i	1.22001	+	0.257759i
$778$	−12.8062	+	6.16712i	−0.459123	+	0.221102i
$779$	−3.37419	−	2.69083i	−0.120893	−	0.0964090i
$780$	0.455066	+	3.52504i	0.0162940	+	0.126217i
$781$	−3.42422	+	9.78587i	−0.122528	+	0.350166i
$782$	54.3974			1.94525
$783$	15.4212	+	23.3492i	0.551110	+	0.834433i
$784$	−4.21271			−0.150454
$785$	5.94703	−	16.9956i	0.212259	−	0.606601i
$786$	−0.166624	−	1.29071i	−0.00594328	−	0.0460379i
$787$	−20.8008	−	16.5881i	−0.741469	−	0.591302i	0.178201	−	0.983994i	$-0.442972\pi$
$787$	−20.8008	−	16.5881i	−0.741469	−	0.591302i	−0.919670	+	0.392692i	$0.871544\pi$
$788$	3.83690	−	1.84775i	0.136684	−	0.0658235i
$789$	−15.8308	−	3.34467i	−0.563592	−	0.119074i
$790$	4.47222	+	5.60799i	0.159114	+	0.199523i
$791$	9.69225	−	6.09005i	0.344617	−	0.216537i
$792$	−5.86184	+	1.53912i	−0.208291	+	0.0546903i
$793$	0.331580	+	2.94286i	0.0117748	+	0.104504i
$794$	26.2900	+	16.5191i	0.932998	+	0.586242i
$795$	18.6593	−	30.7914i	0.661778	−	1.09206i
$796$	−11.1709	+	2.54968i	−0.395941	+	0.0903709i
$797$	3.37422	−	1.18069i	0.119521	−	0.0418222i	−0.269856	−	0.962901i	$-0.586976\pi$
$797$	3.37422	−	1.18069i	0.119521	−	0.0418222i	0.389377	+	0.921078i	$0.372690\pi$
$798$	−1.98760	−	3.05244i	−0.0703602	−	0.108055i
$799$	3.23405	+	14.1693i	0.114412	+	0.501273i
$800$	7.06194	−	7.06194i	0.249677	−	0.249677i
$801$	2.24133	−	28.0170i	0.0791934	−	0.989931i
$802$	−27.5430	+	3.10335i	−0.972576	+	0.109583i
$803$	1.76932	+	0.403835i	0.0624378	+	0.0142510i
$804$	−15.4025	+	15.9094i	−0.543206	+	0.561081i
$805$	31.7188	−	25.2949i	1.11794	−	0.891528i
$806$	8.17534	−	16.9763i	0.287964	−	0.597964i
$807$	6.06763	+	7.36095i	0.213591	+	0.259118i
$808$	12.6334	−	15.8418i	0.444442	−	0.557313i
$809$	0.733011	−	6.50565i	0.0257713	−	0.228727i	−0.974224	−	0.225584i	$-0.927571\pi$
$809$	0.733011	−	6.50565i	0.0257713	−	0.228727i	0.999995	−	0.00314277i	$-0.00100038\pi$
$810$	16.3114	+	22.5729i	0.573125	+	0.793131i
$811$			30.0526i			1.05529i	0.849465	+	0.527645i	$0.176925\pi$
$811$			30.0526i			1.05529i	−0.849465	+	0.527645i	$0.823075\pi$
$812$	−2.75206	−	13.6790i	−0.0965784	−	0.480040i
$813$	−36.5187	+	8.95938i	−1.28077	+	0.314219i
$814$	16.1342	+	5.64561i	0.565504	+	0.197878i
$815$	7.17719	+	0.808675i	0.251406	+	0.0283266i
$816$	−12.2743	+	26.5799i	−0.429685	+	0.930482i
$817$	−0.758459	−	1.57496i	−0.0265351	−	0.0551007i
$818$	−14.4122	−	6.94057i	−0.503912	−	0.242671i
$819$	7.54367	+	3.33653i	0.263597	+	0.116588i
$820$	−8.75391	−	13.9318i	−0.305700	−	0.486518i
$821$	−7.11158	+	31.1579i	−0.248196	+	1.08742i	0.685140	+	0.728412i	$0.259741\pi$
$821$	−7.11158	+	31.1579i	−0.248196	+	1.08742i	−0.933336	+	0.359005i	$0.883116\pi$
$822$	−5.41661	−	14.7116i	−0.188926	−	0.513124i
$823$	−10.7333	+	17.0819i	−0.374139	+	0.595439i	−0.979726	−	0.200340i	$-0.935795\pi$
$823$	−10.7333	+	17.0819i	−0.374139	+	0.595439i	0.605587	+	0.795779i	$0.292938\pi$
$824$	13.4072	+	13.4072i	0.467063	+	0.467063i
$825$	1.74488	+	3.47812i	0.0607488	+	0.121093i
$826$	−4.06504	−	11.6172i	−0.141441	−	0.404215i
$827$	−8.59715	−	24.5693i	−0.298952	−	0.854357i	−0.991162	−	0.132660i	$-0.957648\pi$
$827$	−8.59715	−	24.5693i	−0.298952	−	0.854357i	0.692209	−	0.721697i	$-0.256637\pi$
$828$	−21.9838	+	18.7270i	−0.763989	+	0.650807i
$829$	3.76700	+	3.76700i	0.130833	+	0.130833i	0.769491	−	0.638658i	$-0.220510\pi$
$829$	3.76700	+	3.76700i	0.130833	+	0.130833i	−0.638658	+	0.769491i	$0.720510\pi$
$830$	14.6835	−	23.3686i	0.509670	−	0.811135i
$831$	−39.6898	+	14.6133i	−1.37682	+	0.506929i
$832$	−0.148027	+	0.648550i	−0.00513192	+	0.0224844i
$833$	−1.51658	−	2.41363i	−0.0525465	−	0.0836273i
$834$	14.4268	+	11.1278i	0.499559	+	0.385325i
$835$	−32.3920	−	15.5992i	−1.12097	−	0.539832i
$836$	−0.266598	−	0.553597i	−0.00922049	−	0.0191466i
$837$	−2.45801	−	50.5820i	−0.0849611	−	1.74837i
$838$	−30.8103	−	3.47148i	−1.06432	−	0.119920i
$839$	45.6449	+	15.9718i	1.57584	+	0.551409i	0.969773	−	0.244008i	$-0.0784624\pi$
$839$	45.6449	+	15.9718i	1.57584	+	0.551409i	0.606063	+	0.795417i	$0.292748\pi$
$840$	3.02876	+	12.3453i	0.104502	+	0.425953i
$841$	26.7437	−	11.2150i	0.922196	−	0.386724i
$842$		−	18.3457i		−	0.632233i
$843$	−3.81183	+	39.5785i	−0.131286	+	1.36316i
$844$	2.89715	−	25.7130i	0.0997242	−	0.885076i
$845$	13.0174	−	16.3233i	0.447813	−	0.561540i
$846$	−18.0312	−	13.4482i	−0.619925	−	0.462359i
$847$	10.2629	−	21.3111i	0.352638	−	0.732260i
$848$	−45.7997	+	36.5241i	−1.57277	+	1.25424i
$849$	33.0338	+	31.9814i	1.13372	+	1.09760i
$850$	10.6689	+	2.43511i	0.365941	+	0.0835236i
$851$	−74.0872	+	8.34762i	−2.53968	+	0.286153i
$852$	−14.6911	−	4.87521i	−0.503308	−	0.167022i
$853$	−13.2989	+	13.2989i	−0.455345	+	0.455345i	−0.897124	−	0.441779i	$-0.854347\pi$
$853$	−13.2989	+	13.2989i	−0.455345	+	0.455345i	0.441779	+	0.897124i	$0.354347\pi$
$854$	−2.57475	−	11.2807i	−0.0881062	−	0.386018i
$855$	1.76741	−	1.88571i	0.0604442	−	0.0644898i
$856$	−1.88484	+	0.659535i	−0.0644226	+	0.0225424i
$857$	21.8609	−	4.98961i	0.746754	−	0.170442i	0.167822	−	0.985817i	$-0.446327\pi$
$857$	21.8609	−	4.98961i	0.746754	−	0.170442i	0.578932	+	0.815375i	$0.303469\pi$
$858$	3.46922	+	2.10232i	0.118437	+	0.0717720i
$859$	18.0755	+	11.3576i	0.616730	+	0.387517i	0.803860	−	0.594818i	$-0.202776\pi$
$859$	18.0755	+	11.3576i	0.616730	+	0.387517i	−0.187131	+	0.982335i	$0.559919\pi$
$860$	−0.746184	−	6.62257i	−0.0254447	−	0.225828i
$861$	−38.1799	+	0.618011i	−1.30117	+	0.0210618i
$862$	−21.1660	+	13.2995i	−0.720918	+	0.452983i
$863$	−23.5034	−	29.4724i	−0.800066	−	1.00325i	−0.999727	−	0.0233862i	$-0.992555\pi$
$863$	−23.5034	−	29.4724i	−0.800066	−	1.00325i	0.199660	−	0.979865i	$-0.436016\pi$
$864$	−7.54332	−	26.9459i	−0.256629	−	0.916719i
$865$	−5.28231	+	2.54383i	−0.179604	+	0.0864927i
$866$	−13.3862	−	10.6752i	−0.454882	−	0.362757i
$867$	9.55512	−	1.23352i	0.324509	−	0.0418925i
$868$	−8.34026	+	23.8351i	−0.283087	+	0.809016i
$869$	2.80804			0.0952562
$870$	26.1243	−	12.2708i	0.885696	−	0.416020i
$871$	−13.5668			−0.459694
$872$	5.84355	−	16.6999i	0.197888	−	0.565531i
$873$	5.62656	+	14.5510i	0.190430	+	0.492477i
$874$	6.10858	+	4.87143i	0.206626	+	0.164778i
$875$	27.1781	−	13.0883i	0.918787	−	0.442465i
$876$	−0.560091	+	2.65099i	−0.0189237	+	0.0895686i
$877$	16.0258	+	20.0958i	0.541154	+	0.678586i	0.974950	−	0.222425i	$-0.0713974\pi$
$877$	16.0258	+	20.0958i	0.541154	+	0.678586i	−0.433796	+	0.901011i	$0.642826\pi$
$878$	−57.2498	+	35.9724i	−1.93209	+	1.21401i
$879$	−0.531640	−	32.8440i	−0.0179318	−	1.10780i
$880$	1.20228	+	10.6705i	0.0405289	+	0.359704i
$881$	43.6456	+	27.4243i	1.47046	+	0.923949i	0.999118	+	0.0419974i	$0.0133721\pi$
$881$	43.6456	+	27.4243i	1.47046	+	0.923949i	0.471339	+	0.881952i	$0.343771\pi$
$882$	4.20924	+	1.32160i	0.141732	+	0.0445005i
$883$	−3.39773	+	0.775510i	−0.114343	+	0.0260980i	−0.279309	−	0.960201i	$-0.590106\pi$
$883$	−3.39773	+	0.775510i	−0.114343	+	0.0260980i	0.164967	+	0.986299i	$0.447248\pi$
$884$	3.69350	−	1.29241i	0.124226	−	0.0434685i
$885$	7.31819	−	4.76525i	0.245998	−	0.160182i
$886$	7.50268	+	32.8714i	0.252057	+	1.10434i
$887$	−21.7214	+	21.7214i	−0.729332	+	0.729332i	−0.970487	−	0.241155i	$-0.922474\pi$
$887$	−21.7214	+	21.7214i	−0.729332	+	0.729332i	0.241155	+	0.970487i	$0.422474\pi$
$888$	7.35744	−	22.1711i	0.246899	−	0.744012i
$889$	6.43766	−	0.725351i	0.215912	−	0.0243275i
$890$	−28.2640	−	6.45108i	−0.947412	−	0.216241i
$891$	10.8903	+	0.517220i	0.364838	+	0.0173275i
$892$	14.9665	−	11.9354i	0.501116	−	0.399627i
$893$	−0.905726	+	1.88076i	−0.0303090	+	0.0629372i
$894$	−10.2770	+	8.47136i	−0.343715	+	0.283325i
$895$	6.12954	−	7.68620i	0.204888	−	0.256921i
$896$	3.28323	−	29.1395i	0.109685	−	0.973483i
$897$	−17.6117	−	1.69619i	−0.588036	−	0.0566341i
$898$			0.747116i			0.0249316i
$899$	−51.9844	−	7.22298i	−1.73378	−	0.240900i
$900$	−5.14997	+	2.68879i	−0.171666	+	0.0896265i
$901$	−37.4140	−	13.0917i	−1.24644	−	0.436149i
$902$	−18.6605	−	2.10254i	−0.621328	−	0.0700068i
$903$	−14.0416	−	6.48426i	−0.467277	−	0.215783i
$904$	−3.33788	−	6.93119i	−0.111016	−	0.230528i
$905$	12.5951	+	6.06550i	0.418676	+	0.201624i
$906$	16.3025	−	21.1356i	0.541614	−	0.702182i
$907$	8.72468	+	13.8852i	0.289698	+	0.461052i	0.959588	−	0.281408i	$-0.0908016\pi$
$907$	8.72468	+	13.8852i	0.289698	+	0.461052i	−0.669890	+	0.742460i	$0.733659\pi$
$908$	5.64106	−	24.7151i	0.187205	−	0.820199i
$909$	−30.2201	+	20.3818i	−1.00234	+	0.676022i
$910$	4.52661	−	7.20405i	0.150056	−	0.238812i
$911$	11.4146	+	11.4146i	0.378182	+	0.378182i	0.870446	−	0.492264i	$-0.163830\pi$
$911$	11.4146	+	11.4146i	0.378182	+	0.378182i	−0.492264	+	0.870446i	$0.663830\pi$
$912$	−3.75864	+	1.88560i	−0.124461	+	0.0624386i
$913$	−3.56846	−	10.1981i	−0.118099	−	0.337507i
$914$	4.96970	+	14.2026i	0.164383	+	0.469779i
$915$	7.33826	−	3.68140i	0.242595	−	0.121703i
$916$	4.56143	+	4.56143i	0.150714	+	0.150714i
$917$	−0.568520	+	0.904795i	−0.0187742	+	0.0298790i
$918$	20.6027	−	22.7073i	0.679990	−	0.749453i
$919$	0.854390	−	3.74333i	0.0281837	−	0.123481i	−0.958879	−	0.283815i	$-0.908400\pi$
$919$	0.854390	−	3.74333i	0.0281837	−	0.123481i	0.987063	+	0.160334i	$0.0512571\pi$
$920$	−14.5063	−	23.0866i	−0.478259	−	0.761144i
$921$	2.74348	−	3.55682i	0.0904008	−	0.117201i
$922$	47.9121	+	23.0733i	1.57790	+	0.759877i
$923$	−4.11470	−	8.54427i	−0.135437	−	0.281238i
$924$	−4.93564	−	2.27922i	−0.162371	−	0.0749808i
$925$	−14.9043	−	1.67931i	−0.490051	−	0.0552155i
$926$	−30.7261	−	10.7515i	−1.00972	−	0.353317i
$927$	−15.7863	−	30.2362i	−0.518489	−	0.993087i
$928$	−28.8917	+	2.50068i	−0.948417	+	0.0820887i
$929$			40.7797i			1.33794i	0.743290	+	0.668970i	$0.233264\pi$
$929$			40.7797i			1.33794i	−0.743290	+	0.668970i	$0.766736\pi$
$930$	−51.9946	−	5.00763i	−1.70497	−	0.164207i
$931$	0.0458413	−	0.406853i	0.00150239	−	0.0133341i
$932$	8.83208	−	11.0751i	0.289304	−	0.362776i
$933$	26.6324	−	21.9531i	0.871907	−	0.718713i
$934$	−13.9080	+	28.8803i	−0.455084	+	0.944992i
$935$	−5.68075	+	4.53024i	−0.185780	+	0.148155i
$936$	2.79593	−	4.78693i	0.0913878	−	0.156466i
$937$	−31.6163	−	7.21621i	−1.03286	−	0.235743i	−0.327692	−	0.944785i	$-0.606271\pi$
$937$	−31.6163	−	7.21621i	−1.03286	−	0.235743i	−0.705167	+	0.709041i	$0.749128\pi$
$938$	52.6737	−	5.93490i	1.71986	−	0.193781i
$939$	6.61696	−	19.9397i	0.215936	−	0.650707i
$940$	−5.62751	+	5.62751i	−0.183549	+	0.183549i
$941$	1.18385	+	5.18681i	0.0385926	+	0.169085i	0.990552	−	0.137140i	$-0.0437911\pi$
$941$	1.18385	+	5.18681i	0.0385926	+	0.169085i	−0.951959	+	0.306225i	$0.900934\pi$
$942$	25.7112	−	16.7419i	0.837716	−	0.545480i
$943$	77.3098	−	27.0519i	2.51755	−	0.880931i
$944$	−13.8526	+	3.16176i	−0.450863	+	0.102907i
$945$	1.45436	−	22.8208i	0.0473103	−	0.742360i
$946$	−6.44032	−	4.04672i	−0.209393	−	0.131570i
$947$	−5.03475	−	44.6846i	−0.163607	−	1.45205i	−0.760293	−	0.649580i	$-0.774945\pi$
$947$	−5.03475	−	44.6846i	−0.163607	−	1.45205i	0.596686	−	0.802475i	$-0.296484\pi$
$948$	0.0678526	+	4.19184i	0.00220375	+	0.136145i
$949$	−1.40559	+	0.883191i	−0.0456274	+	0.0286696i
$950$	0.979999	+	1.22888i	0.0317954	+	0.0398701i
$951$	7.45845	−	35.3019i	0.241857	−	1.14474i
$952$	12.6087	−	6.07202i	0.408650	−	0.196795i
$953$	27.9048	+	22.2534i	0.903926	+	0.720857i	0.960717	−	0.277529i	$-0.0895155\pi$
$953$	27.9048	+	22.2534i	0.903926	+	0.720857i	−0.0567912	+	0.998386i	$0.518087\pi$
$954$	57.2201	−	22.1258i	1.85257	−	0.716349i
$955$	5.46449	−	15.6166i	0.176827	−	0.505342i
$956$	−17.9181			−0.579513
$957$	2.62076	−	10.9910i	0.0847173	−	0.355289i
$958$	22.2714			0.719555
$959$	−4.25145	+	12.1499i	−0.137286	+	0.392342i
$960$	1.82899	−	0.236114i	0.0590306	−	0.00762056i
$961$	50.0252	+	39.8937i	1.61371	+	1.28689i
$962$	−14.0872	+	6.78402i	−0.454188	+	0.218725i
$963$	3.59043	−	0.116266i	0.115700	−	0.00374661i
$964$	−10.6629	−	13.3708i	−0.343428	−	0.430645i
$965$	−17.8102	+	11.1909i	−0.573330	+	0.360247i
$966$	69.1201	−	1.11884i	2.22390	−	0.0359979i
$967$	−3.77346	−	33.4904i	−0.121346	−	1.07698i	−0.895834	−	0.444389i	$-0.853421\pi$
$967$	−3.77346	−	33.4904i	−0.121346	−	1.07698i	0.774487	−	0.632589i	$-0.218008\pi$
$968$	−13.4603	−	8.45765i	−0.432630	−	0.271839i
$969$	−2.43345	−	1.47465i	−0.0781737	−	0.0473726i
$970$	15.6884	−	3.58077i	0.503724	−	0.114972i
$971$	16.1225	−	5.64150i	0.517395	−	0.181044i	−0.0589345	−	0.998262i	$-0.518770\pi$
$971$	16.1225	−	5.64150i	0.517395	−	0.181044i	0.576329	+	0.817218i	$0.304485\pi$
$972$	−0.508956	+	16.2695i	−0.0163248	+	0.521844i
$973$	−3.32894	−	14.5850i	−0.106721	−	0.467575i
$974$	−15.4687	+	15.4687i	−0.495650	+	0.495650i
$975$	−3.37823	−	1.12106i	−0.108190	−	0.0359027i
$976$	−13.2739	+	1.49561i	−0.424888	+	0.0478734i
$977$	20.1415	+	4.59718i	0.644385	+	0.147077i	0.532211	−	0.846612i	$-0.321361\pi$
$977$	20.1415	+	4.59718i	0.644385	+	0.147077i	0.112174	+	0.993689i	$0.464218\pi$
$978$	8.84205	+	8.56036i	0.282737	+	0.273730i
$979$	−8.87328	+	7.07620i	−0.283591	+	0.226156i
$980$	0.677264	−	1.40635i	0.0216344	−	0.0449243i
$981$	−19.0288	+	25.5136i	−0.607544	+	0.814586i
$982$	17.8378	−	22.3679i	0.569226	−	0.713787i
$983$	−5.02289	+	44.5794i	−0.160205	+	1.42186i	0.614189	+	0.789159i	$0.289483\pi$
$983$	−5.02289	+	44.5794i	−0.160205	+	1.42186i	−0.774394	+	0.632703i	$0.781945\pi$
$984$	−2.46022	+	25.5447i	−0.0784291	+	0.814336i
$985$		−	7.23315i		−	0.230467i
$986$	−19.1631	−	25.3477i	−0.610278	−	0.807234i
$987$	4.40077	+	17.9377i	0.140078	+	0.570963i
$988$	0.530501	+	0.185630i	0.0168775	+	0.00590569i
$989$	32.9670	+	3.71448i	1.04829	+	0.118114i
$990$	2.14623	−	11.0389i	0.0682117	−	0.350839i
$991$	10.6671	+	22.1505i	0.338852	+	0.703633i	0.998865	−	0.0476206i	$-0.0151638\pi$
$991$	10.6671	+	22.1505i	0.338852	+	0.703633i	−0.660014	+	0.751254i	$0.729450\pi$
$992$	47.2858	+	22.7717i	1.50133	+	0.723001i
$993$	−24.1940	−	18.6616i	−0.767774	−	0.592207i
$994$	19.7133	+	31.3735i	0.625267	+	0.995107i
$995$	−4.33053	+	18.9733i	−0.137287	+	0.601494i
$996$	15.1374	−	5.57342i	0.479648	−	0.176600i
$997$	−27.1748	+	43.2484i	−0.860634	+	1.36969i	0.0676073	+	0.997712i	$0.478463\pi$
$997$	−27.1748	+	43.2484i	−0.860634	+	1.36969i	−0.928241	+	0.371979i	$0.878679\pi$
$998$	−25.2378	−	25.2378i	−0.798887	−	0.798887i
$999$	−24.5755	+	34.0881i	−0.777534	+	1.07850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.k.a.8.7	yes	96
3.2	odd	2	inner	87.2.k.a.8.2	✓	96
29.11	odd	28	inner	87.2.k.a.11.2	yes	96
87.11	even	28	inner	87.2.k.a.11.7	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.k.a.8.2	✓	96	3.2	odd	2	inner
87.2.k.a.8.7	yes	96	1.1	even	1	trivial
87.2.k.a.11.2	yes	96	29.11	odd	28	inner
87.2.k.a.11.7	yes	96	87.11	even	28	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.k (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.576259 - 1.64685i) q^{2} +(-0.221759 - 1.71780i) q^{3} +(-0.816387 - 0.651047i) q^{4} +(-1.59790 + 0.769508i) q^{5} +(-2.95675 - 0.624690i) q^{6} +(1.54710 + 1.94000i) q^{7} +(1.41204 - 0.887242i) q^{8} +(-2.90165 + 0.761874i) q^{9} +(0.346463 + 3.07494i) q^{10} +(1.02572 + 0.644501i) q^{11} +(-0.937325 + 1.54676i) q^{12} +(-1.08029 + 0.246570i) q^{13} +(4.08643 - 1.42990i) q^{14} +(1.67621 + 2.57422i) q^{15} +(-1.11217 - 4.87274i) q^{16} +(2.39140 - 2.39140i) q^{17} +(-0.417404 + 5.21762i) q^{18} +(0.482698 - 0.0543871i) q^{19} +(1.80549 + 0.412091i) q^{20} +(2.98944 - 3.08782i) q^{21} +(1.65248 - 1.31781i) q^{22} +(-3.99989 + 8.30586i) q^{23} +(-1.83723 - 2.22884i) q^{24} +(-1.15631 + 1.44997i) q^{25} +(-0.216464 + 1.92117i) q^{26} +(1.95221 + 4.81548i) q^{27} -2.59103i q^{28} +(5.27938 - 1.06215i) q^{29} +(5.20529 - 1.27705i) q^{30} +(-9.19909 - 3.21890i) q^{31} +(-5.35125 - 0.602941i) q^{32} +(0.879658 - 1.90490i) q^{33} +(-2.56022 - 5.31635i) q^{34} +(-3.96496 - 1.90942i) q^{35} +(2.86488 + 1.26712i) q^{36} +(4.30274 + 6.84777i) q^{37} +(0.188592 - 0.826274i) q^{38} +(0.663123 + 1.80105i) q^{39} +(-1.57355 + 2.50430i) q^{40} +(-6.28241 - 6.28241i) q^{41} +(-3.36249 - 6.70256i) q^{42} +(-1.18857 - 3.39673i) q^{43} +(-0.417782 - 1.19395i) q^{44} +(4.05027 - 3.45024i) q^{45} +(11.3736 + 11.3736i) q^{46} +(-2.28637 + 3.63873i) q^{47} +(-8.12373 + 2.99106i) q^{48} +(0.187557 - 0.821739i) q^{49} +(1.72155 + 2.73983i) q^{50} +(-4.63825 - 3.57762i) q^{51} +(1.04247 + 0.502026i) q^{52} +(-5.08537 - 10.5599i) q^{53} +(9.05537 - 0.440041i) q^{54} +(-2.13494 - 0.240550i) q^{55} +(3.90581 + 1.36670i) q^{56} +(-0.200469 - 0.817117i) q^{57} +(1.29308 - 9.30643i) q^{58} -2.84288i q^{59} +(0.307505 - 3.19285i) q^{60} +(0.299240 - 2.65582i) q^{61} +(-10.6021 + 13.2946i) q^{62} +(-5.96717 - 4.45050i) q^{63} +(0.260480 - 0.540893i) q^{64} +(1.53646 - 1.22529i) q^{65} +(-2.63017 - 2.54638i) q^{66} +(11.9366 + 2.72445i) q^{67} +(-3.50922 + 0.395394i) q^{68} +(15.1548 + 5.02910i) q^{69} +(-5.42938 + 5.42938i) q^{70} +(1.90444 + 8.34388i) q^{71} +(-3.42126 + 3.65026i) q^{72} +(1.41405 - 0.494798i) q^{73} +(13.7568 - 3.13989i) q^{74} +(2.74717 + 1.66476i) q^{75} +(-0.429477 - 0.269859i) q^{76} +(0.336554 + 2.98700i) q^{77} +(3.34819 - 0.0541966i) q^{78} +(1.96273 - 1.23326i) q^{79} +(5.52674 + 6.93032i) q^{80} +(7.83910 - 4.42138i) q^{81} +(-13.9665 + 6.72591i) q^{82} +(-6.97313 - 5.56088i) q^{83} +(-4.45086 + 0.574585i) q^{84} +(-1.98101 + 5.66141i) q^{85} -6.27884 q^{86} +(-2.99531 - 8.83335i) q^{87} +2.02018 q^{88} +(-3.09433 + 8.84308i) q^{89} +(-3.34803 - 8.65843i) q^{90} +(-2.14967 - 1.71431i) q^{91} +(8.67297 - 4.17668i) q^{92} +(-3.48943 + 16.5160i) q^{93} +(4.67492 + 5.86216i) q^{94} +(-0.729452 + 0.458345i) q^{95} +(0.150959 + 9.32607i) q^{96} +(-0.582251 - 5.16762i) q^{97} +(-1.24520 - 0.782413i) q^{98} +(-3.46730 - 1.08865i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{3} - 28 q^{4} - 14 q^{6} - 20 q^{7} - 14 q^{9} - 4 q^{10} - 8 q^{12} - 28 q^{13} - 16 q^{15} - 48 q^{16} - 28 q^{18} - 20 q^{19} + 26 q^{21} - 28 q^{22} + 58 q^{24} - 20 q^{25} + 36 q^{27}+ \cdots + 82 q^{99}+O(q^{100}) \) 96 * q - 12 * q^3 - 28 * q^4 - 14 * q^6 - 20 * q^7 - 14 * q^9 - 4 * q^10 - 8 * q^12 - 28 * q^13 - 16 * q^15 - 48 * q^16 - 28 * q^18 - 20 * q^19 + 26 * q^21 - 28 * q^22 + 58 * q^24 - 20 * q^25 + 36 * q^27 + 96 * q^30 - 32 * q^31 + 28 * q^33 - 28 * q^34 + 22 * q^36 - 4 * q^37 - 40 * q^39 - 48 * q^40 - 14 * q^42 - 32 * q^43 + 42 * q^45 + 120 * q^46 - 20 * q^48 + 4 * q^49 - 14 * q^51 + 72 * q^52 - 30 * q^54 + 148 * q^55 + 112 * q^58 + 20 * q^60 + 12 * q^61 - 14 * q^63 + 224 * q^64 - 32 * q^66 + 28 * q^67 + 10 * q^69 + 52 * q^70 - 44 * q^72 + 16 * q^73 - 144 * q^75 - 100 * q^76 - 102 * q^78 - 60 * q^79 - 146 * q^81 - 108 * q^82 - 64 * q^84 - 104 * q^85 - 70 * q^87 - 312 * q^88 - 96 * q^90 - 112 * q^91 - 70 * q^93 + 56 * q^94 - 168 * q^96 + 32 * q^97 + 82 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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